Matrices

CBSE Class 12 Mathematics · 156 board questions from this chapter; 154 listed below, 2023–2026

• If matrix A= [-p, q; r, p] is such that A^2=I, then:2026
• If A= [sin θ, cos θ; - cos θ, sin θ] and A+A^′=I, then θ is equal to:2026
• For any square matrix A with real entries, if A + A' is a symmetric matrix then:2026
• If A=[a_ij] is a 2 × 2 matrix whose elements are given by a_ij=(|i-3 j|)/2, then A' is:2026
• If A and B are square matrices of same order, then which of the following statements is/are always true? (i) (A+B)(A-B)=A^2-B^2…2026
• Let A=[a_ij] be a 2 × 2 matrix whose elements are given by a_ij=((i+2 j)^2)/3. Then A^′ is given by:2026
• If A is a square matrix such that A^2=A, then (A-I)^3-A is equal to:2026
• Let A=[a_ij] be a 2 × 2 matrix whose elements are given by a_ij=((2 i-j)^2)/3. Then A^′ is:2026
• Which of the following cannot be the order of a row-matrix?2026
• If A is a symmetric matrix, then for any matrix B of order same as A, BAB' is a/an:2026
• A matrix B=[b_ij]_m × m is said to be a diagonal matrix, if:2026
• If A^2=4 A+3 I and A^-1=xA+yI, then the value of (x+y) is:2026
• If A and B are skew-symmetric matrices of same order, then AB^′+BA^′ is a/an:2026
• Which of the following properties is/are true for two matrices of suitable orders? (i) (A+B)^′=A^′+B^′ (ii) (A-B)^′=B^′-A^′ (iii)…2026
• If A= [1, a, b; -1, 2, c; 0, 5, 3] is a symmetric matrix, then the value of 3 a+b+c is2026
• If A= [cos x, - sin x; sin x, cos x] and A+A^′=I, then the value of x ∈[0, (π)/2] is2026
• Let A= [0, -3, 4; 1, 0, 2] and B= [-3, 0, 1; 2, 4, 0]. If A+B+C=O, then matrix C is:2026
• If [4; 1; 3] A= [-4, 8, 4; -1, 2, 1; -3, 6, 3], then order of A must be:2026
• For a square matrix A, (3 A)^-1=2026
• If a square matrix A is such that A^2=A and (I-A)^3=xA+I, then value of x must be:2026
• If A is a non-singular matrix, then which of the following is not true?2026
• If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew symmetric?2026
• If A=[a_ij]_3 × 3 is a scalar matrix then which of the following must be true?2026
• If a matrix X is such that [2 1] X = [3 4 5], then the order of matrix X is:2026
• If A= [tan x, cot x; - cot x, tan x] and A+A^′=2 I, then value of x ∈[0, (π)/2] is2026
• If A and B are symmetric matrics of same order, then (AB-BA) is a2026
• Which of the following cannot be an order of a column-matrix?2026
• If a matrix B is such that B [1, 2, 3] = [1, 2, 3; 0, 1, 1; 2, 0, 1], then the order of matrix B is: matrix B is:2026
• If A= [1/2 cos x, - sin x; sin x, 1/2 cos x] and A+A^′=I, then value of x ∈[(-π)/2, (π)/2] is2026
• If A and B are symmetric matrices of same order, then which of the following matrices is a skew-symmetric matrix?2026
• Assertion: If A and B are two square matrices such that AB and BA are defined, then it is not necessary that AB=BA. Reason (R):…2026
• If A= [1, 2, 2; 2, 1, 2; 2, 2, 1], then compute A^2-4 A-5 I.2026
• If A= [2, 0, 1; 2, 1, 3; 1, -1, 0], then compute A^2-5 A+4 I.2026
• If A= [3, 2, 0; 1, 4, 0; 0, 0, 5], then compute A^2-7 A+10 I.2026
• Find cost (per kg) of each fertilizer A, B and C that the farmer needs to buy, such that 1 kg each of fertilizer A and C added to…2026
• A man goes to buy fruits from the market. The shopkeeper informs him that 4 apples, 3 oranges and 2 bananas cost ₹ 60; 2 apples,…2026
• Three students A, B and C go to a book-store to buy art books, story books and puzzle solving books. A buys one of each type of…2026
• If P= [1, -1, 0; 2, 3, 4; 0, 1, 2] and Q= [2, 2, -4; -4, 2, -4; 2, -1, 5], find (QP) and hence solve the following system of…2026
• If A= [0, 2, 1; -2, -1, -2; 1, -1, 0], find A^-1 and use it to solve the following system of equations: -2 y+z=7,2 x-y-z=8, x-2…2026
• On the inauguration day of a new showroom, a lucky draw was organized and some vouchers of ₹ 1,000 and ₹ 500 were given to the…2026
• A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than…2026
• Let both AB^′ and B^′ A be defined for matrices A and B. If order of A is n × m, then the order of B is:2025
• If A= [5, 0, 0; 0, 5, 0; 0, 0, 5], then A^3 is:2025
• If A= [0, -3, 8; 3, 0, 5; -8, -5, 0], then A is a:2025
• If A and B are square matrices of same order such that AB=A and BA=B, then A^2+B^2 is equal to:2025
• If A= [-1, 0, 0; 0, 3, 0; 0, 0, 5], then A is a/an:2025
• If A= [0, 0, -5; 0, 3, 0; 4 · 3, 0, 0], then A is a:2025
• What is the total number of possible matrices of order 3 × 3 with each entry as √2 or √3?2025
• If A and B are two square matrices of the same order, then (A+B)(A-B) is equal to:2025
• If A=kB, where A and B are two square matrices of order n and k is a scalar, then:2025
• If A= [1, 2, 3; -4, 3, 7] and B= [4, 3; -1, 2; 0, 5], then the correct statement is:2025
• Let P be a skew-symmetric matrix of order 3. If det(P)=α, then (2025)^α is2025
• The matrix A= [√3, 0, 0; 0, √2, 0; 0, 0, √5] is a/an:2025
• If A= [1, 12, 4 y; 6 x, 5, 2 x; 8 x, 4, 6] is a symmetric matrix, then (2 x+y) is2025
• If A and B are square matrices of same order, then (AB^T-BA^T) is a2025
• Sum of two skew-symmetric matrices of same order is always a/an:2025
• If A is a square matrix of order 3 such that det(A)=9, then det(9 A^-1) is equal to2025
• If [x+y, 3 y; 3 x, x+3] = [9, 4 x+y; x+6, y], then (x-y)=?2025
• If M and N are square matrices of order 3 such that det(M)=m and MN=mI, then det(N) is equal to:2025
• If [2 x-1, 3 x; 0, y^2-1] = [x+3, 12; 0, 35], then the value of (x-y) is:2025
• If A and B are invertible matrices of order 3 × 3 such that det(A)=4 and det[(AB)^-1]=1/20, then det(B) is equal to:2025
• If a matrix A is both symmetric and skew-symmetric, then A is a:2025
• Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4 AB+3(AB+BA)-4 BA, where A and B are both matrices of order 2…2025
• Let A and B be two matrices of suitable orders. Then, which of the following is not correct?2025
• If [4+x, x-1; -2, 3] is a singular matrix, then the value of x is:2025
• Which of the following can be both a symmetric and skew-symmetric matrix?2025
• Let A= [1, -2, -1; 0, 4, -1; -3, 2, 1], B= [-2; -5; -7], C= [9, 8, 7], which of the following is defined?2025
• Let A be a matrix of order m × n and B is a matrix such that A^T B and B A^T are defined. Then, the order of B is:2025
• The matrix [0, 1, -2; -1, 0, -7; 2, 7, 0] is a:2025
• A system of linear equations is represented as AX=B, where A is coefficient matrix, X is variable matrix and B is the constant…2025
• If A= [-1, 0, 0; 0, 1, 0; 0, 0, 1], then A^-1 is2025
• If A= [7, 0, x; 0, 7, 0; 0, 0, y] is a scalar matrix, then y^x is equal to2025
• Let A=[a_ij] be a square matrix of order 3 such that a_ij= j-2 i. Then which of the following is true?2025
• If A and B are invertible matrices, then which of the following is not correct?2025
• If A and B are square matrices of order m such that A^2-B^2=(A-B)(A+B), then which of the following is always correct?2025
• Assertion: A =diag [3, 5, 2] is a scalar matrix of order 3 × 3. Reason (R): If a diagonal matrix has all non-zero elements equal,…2025
• If A= [2, -2; -2, 2] and A^2=kA, then find the value of k.2025
• If [3, -1; 0, 1; 2, -3] A= [2; -5; -17], then find matrix A.2025
• If A= [1, 0; -1, 5], then find the value of K if A^2=6 A+K I_2, where I_2 is an identity matrix.2025
• If A= [2, 3; -1, 2], then show that A^2-4 A+7 I=0.2025
• Let A= [1; 4; -2] and C= [3, 4, 2; 12, 16, 8; -6, -8, -4] be two matrices. Then, find the matrix B if AB=C.2025
• Find the value of x, if [1, x, 1] [1, 3, 2; 2, 5, 1; 15, 3, 2] [1; 2; x] =O.2025
• If A= [1, -1, 0], B= [2, 0, 1; -1, 3, 4; 0, 5, 1] and C= [2; 3; 4], are three matrices, then find ABC.2025
• Let 2 x+5 y-1=0 and 3 x+2 y-7=0 represent the equations of two lines on which the ants are moving on the ground. Using matrix…2025
• If A is a 3 × 3 invertible matrix, show that for any scalar k ≠ 0, (kA)^-1=1/k A^-1. Hence calculate (3 A)^-1, where A= [2, -1,…2025
• A furniture workshop produces three types of furniture - chairs, tables and beds each day. On a particular day the total number…2025
• Three students run on a racing track such that their speeds add up to 6 km / h. However, double the speed of the third runner…2025
• An amount of ₹ 10,000 is put into three investments at the rate of 10 %, 12 % and 15 % per annum. The combined annual income of…2025
• Given A= [-4, 4, 4; -7, 1, 3; 5, -3, -1] and B= [1, -1, 1; 1, -2, -2; 2, 1, 3], find AB. Hence, solve the system of linear…2025
• A school wants to allocate students into three clubs: Sports, Music and Drama, under following conditions: - The number of…2025
• Three students, Neha, Rani and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads and 2 erasers and…2025
• If A=[a_ij] is an identity matrix, then which of the following is true?2024
• If [a, c, 0; b, d, 0; 0, 0, 5] is a scalar matrix, then the value of a+2 b+3 c+4 d is:2024
• If the sum of all the elements of a 3 × 3 scalar matrix is 9, then the product of all its elements is:2024
• If A= [a, c, -1; b, 0, 5; 1, -5, 0] is a skew-symmetric matrix, then the value of 2 a-(b+c) is:2024
• If A is a square matrix of order 2 and |A|=-2, then value of |5 A^′| is:2024
• If a matrix has 36 elements, the number of possible orders it can have, is:2024
• For the matrix A= [2, -1, 1; λ, 2, 0; 1, -2, 3] to be invertible, the value of λ is:2024
• Given that A^-1=1/7 [2, 1; -3, 2], matrix A is:2024
• If A= [2, 1; -4, -2], then the value of I-A+A^2-A^3+… is:2024
• If inverse of matrix [7, -3, -3; -1, 1, 0; -1, 0, 1] is the matrix [1, 3, 3; 1, λ, 3; 1, 3, 4], then value of λ is:2024
• If A= [3, 1; -1, 2] and A^2+7 I=kA, then the value of k is:2024
• If A= [x, 0; 1, 1] and B= [4, 0; -1, 1], then value of x for which A^2=B is:2024
• If [x, 2, 0] [5; -1; x] = [3, 1] [-2; x], then value of x is:2024
• If A= [1, 3; 3, 4] and A^2-kA-5 I=O, then the value of k is:2024
• If [x+y, 2; 5, xy] = [6, 2; 5, 8], then the value of (24/x+24/y) is:2024
• Let A= [1, -1, 2; 0, 2, -3; 3, -2, 4] and B=1/3 [-2, 0, 1; 9, 2, -3; 6, 1, λ]. If AB=I, then the value of λ is:2024
• Given that [1, x] [4, 0; -2, 0] =0, the value of x is:2024
• The product of matrix P and Q is equal to a diagonal matrix. If the order of matrix Q is 3 × 2, then order of matrix P is:2024
• If for the matrix A= [tan x, 1; -1, tan x], A+A^′=2 √3 I, then the value of x ∈[0, (π)/2] is:2024
• If matrices A and B are of order 1 × 3 and 3 × 1 respectively, then the order of A^′ B^′ is:2024
• The number of all scalar matrices of order 3, with each entry -1,0 or 1, is:2024
• Find the matrix A^2, where A=[a_ij] is a 2 × 2 matrix whose elements are given by a_ij= maximum ( i, j ) - minimum ( i, j ):2024
• For any square matrix A,(A-A^′) is always2024
• If A and B are two skew symmetric matrices, then (AB+BA) is:2024
• If A=[a_ij] be a 3 × 3 matrix, where a_ij=i-3 j, then which of the following is false?2024
• If F(x)= [cos x, - sin x, 0; sin x, cos x, 0; 0, 0, 1] and [F(x)]^2=F(k x), then the value of k is:2024
• If A and B are two non-zero square matrices of same order such that (A+B)^2=A^2+B^2, then:2024
• Assertion: For any symmetric matrix A, B^′ AB is a skew-symmetric matrix. Reason (R): A square matrix P is skew-symmetric if…2024
• Assertion: Every scalar matrix is a diagonal matrix. Reason (R): In a diagonal matrix, all the diagonal elements are 0.2024
• If A= [1, -2, 0; 2, -1, -1; 0, -2, 1], find A^-1 and use it to solve the following system of equations: x-2 y=10,2 x-y-z=8,-2…2024
• If A= [5, 0, 4; 2, 3, 2; 1, 2, 1] and B^-1= [1, 3, 3; 1, 4, 3; 1, 3, 4], find (AB)^-1. Also, find |(AB)^-1|. OR Given A= [1, 1,…2024
• Solve the following system of equations, using matrices: 2/x+3/y+10/z=4, 4/x-6/y+5/z=1, 6/x+9/y-20/z=2 where x, y, z ≠ 0 OR If A=…2024
• Use the product of matrices (1, 2, -3; 3, 2, -2; 2, -1, 1) (0, 1, 2; -7, 7, -7; -7, 5, -4) to solve the following system of…2024
• A scholarship is a sum of money provided to a student to help him or her pay for education. Some students are granted…2024
• If A= [1, 4, x; z, 2, y; -3, -1, 3] is a symmetric matrix, then the value of x+y+z is:2023
• If A= [0, 1; 0, 0], then A^2023 is equal to2023
• If A is a 3 × 4 matrix and B is a matrix such that A^′ B and AB^′ are both defined, then the order of the matrix B is:2023
• If [1, 1, 1; 0, 1, 1; 0, 0, 1] [x; y; z] = [6; 3; 2], then the value of (2 x+y-z) is:2023
• If for a square matrix A, A^2-3 A+I=O and A^-1=xA+yI, then the value of x+y is:2023
• If x [1; 2] +y [2; 5] =[4/9], then:2023
• If [2, 0; 5, 4] =P+Q, where P is a symmetric and Q is a skew symmetric matrix, then Q is equal to2023
• Let A be a skew-symmetric matrix of order 3. If |A|=x, then (2023)^x is equal to:2023
• If A= [5, x; y, 0] and A=A^T, where A^T is the transpose of the matrix A, then2023
• If A is a square matrix and A^2=A, then (I+A)^2-3 A is equal to:2023
• If for a square matrix A, A^2-A+I=O, then A^-1 equals2023
• A and B are skew-symmetric matrices of same order. AB is symmetric, if:2023
• If a matrix A= [1, 2, 3], then the matrix AA^′ (where A^′ is the transpose of A ) is:2023
• For what value of x ∈[0, (π)/2], is A+A^′=√3 I, where A= [cos x, sin x; - sin x, cos x]?2023
• If A=[a_i j] is a square matrix of order 2 such that a_ij= {1, when i ≠ j; 0, when i=j}, then A^2 is2023
• If A= [3, 4; 5, 2] and 2 A+B is a null matrix, then B is equal to:2023
• If A= [1, 0; 2, 1], B= [x, 0; 1, 1] and A=B^2, then x equals2023
• The product [a, b; -b, a] [a, -b; b, a] is equal to:2023
• Number of symmetric matrices of order 3 × 3 with each entry 1 or -1 is2023
• A and B are square matrices of same order. If (A+B)^2=A^2+B^2, then:2023
• If [x, 2; 3, x-1] is a singular matrix, then the product of all possible values of x is:2023
• If A= [0, 1; -1, 0] and (3 I+4 A)(3 I-4 A)=x^2 I, then the value (s) x is/are:2023
• If A is a 2 × 3 matrix such that AB and AB^′ both are defined, then order of the matrix B is2023
• If A= [1, 2, 3; 3, -2, 1; 4, 2, 1], then show that A^3-23 A-40 I=O.2023
• Find the inverse of the matrix A= [1, -1, 2; 0, 2, -3; 3, -2, 4]. Using the inverse, A^-1, solve the system of linear equations…2023
• If A= [-3, -2, -4; 2, 1, 2; 2, 1, 3], B= [1, 2, 0; -2, -1, -2; 0, -1, 1], then find AB and use it to solve the following system…2023
• If A= [1, 2, -2; -1, 3, 0; 0, -2, 1] and B^-1= [3, -1, 1; -15, 6, -5; 5, -2, 2], find (AB)^-1. OR Solve the following system of…2023
• If A= [1, 0, 2; 0, 2, 1; 2, 0, 3], then show that A^3-6 A^2+7 A+2 I=O. OR If A= [3, 2; 5, -7], then find A^-1 and use it to solve…2023
• Gautam buys 5 pens, 3 bags and 1 instrument box and pays a sum of ₹ 160. From the same shop, Vikram buys 2 pens, 1 bag and 3…2023

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