Matrices questions
472 published questions with worked solutions.
- Let be a real number. Consider the matrix A = pmatrix & 0 & 1 2 & 1 & -2 3 & 1 & -2 pmatrix . If A^7 - ( - 1)A^6 - A^5 is a...
- If M = pmatrix 5 2 & 3 2 - 3 2 & - 1 2 pmatrix , then which of the following matrices is equal to M^ 2022 ?
- Let R = pmatrix a & 3 & b c & 2 & d 0 & 5 & 0 pmatrix : a, b, c, d 0, 3, 5, 7, 11, 13, 17, 19 . Then the number of invertible...
- Let A = bmatrix 1 & 2 -2 & -5 bmatrix . Let , R be such that A^ 2 + A = 2I. Then + is equal to
- Let S be the set containing all 3 3 matrices with entries from −1, 0, 1 . The total number of matrices A S such that the sum of...
- Let A and B be two 3 3 matrices such that AB = I and |A| = 1/8. Then |adj(B adj(2A))| is equal to
- Let A be a matrix of order 2 2, whose entries are from the set 0, 1, 3, 4, 5 . If the sum of all the entries of A is a prime...
- Let A and B be any two 3 3 symmetric and skew symmetric matrices respectively. Then which of the following is NOT true ?
- Let the matrix A = bmatrix 0 & 1 & 0 0 & 0 & 1 1 & 0 & 0 bmatrix and the matrix B_ 0 = A^ 49 + 2A^ 98 . If B_ n = Adj(B_ n-1 )...
- Let A = bmatrix 1 & -1 2 & bmatrix and B = bmatrix & 1 1 & 0 bmatrix , , R. Let _ 1 be the value of which satisfies (A + B)^ 2 =...
- Let A = bmatrix 1 + i & 1 -i & 0 bmatrix where i^ 2 = −1. Then the number of elements in the set n 1, 2, …, 100 : A^ n = A is...
- Let A be a matrix of order 3 3 and det (A) = 2. Then det (det (A) adj (5 adj (A^ 3 ))) is equal to _____.
- Which of the following matrices can NOT be obtained from the matrix bmatrix -1 & 2 1 & -1 bmatrix by a single elementary row...
- If the system of equations x + y + z = 6, 2x + 5y + z = , x + 2y + 3z = 14 has infinitely many solutions, then + is equal to
- Let x = [1; 1; 1] and A = bmatrix -1 & 2 & 3 0 & 1 & 6 0 & 0 & -1 bmatrix . For k N, if XᵀA^ k X = 33, then k is equal to _____.
- Let A and B be two 3 3 non-zero real matrices such that AB is a zero matrix. Then
- Let A = bmatrix 2 & -1 0 & 2 bmatrix . If B = I - ^ 5 C_ 1 ( A) + ^ 5 C_ 2 ( A)^ 2 − … − ^ 5 C_ 5 ( A)^ 5 , then the sum of all...
- Let M = bmatrix 0 & - & 0 bmatrix , where is a non-zero real number and N = _ k=1 ^ 49 M^ 2k . If (I - M^ 2 )N = −2I, then the...
- If the system of linear equations 2x + y − z = 7, x − 3y + 2z = 1, x + 4y + z = k, where , k R has infinitely many solutions,...
- If B= bmatrix 3 & 2 & 0 2 & 4 & 0 1 & 1 & 0 bmatrix , then what is adjoint of B equal to?
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