Matrices questions
472 published questions with worked solutions.
- If P = bmatrix 1 & & 3 1 & 3 & 3 2 & 4 & 4 bmatrix is the adjoint of a 3 × 3 matrix A and |A| = 4, then α is equal to -
- For some , R, let A = bmatrix & 2 1 & 2 bmatrix and B = bmatrix 1 & 1 1 & bmatrix be such that A^2 - 4A + 2I = B^2 - 3B + I = O....
- If A = bmatrix 2 & 3 3 & 5 bmatrix , then the determinant of the matrix (A^ 2025 - 3A^ 2024 + A^ 2023 ) is
- Let A be a 3 3 matrix such that A+A^T = O. If A bmatrix 1 -1 0 bmatrix = bmatrix 3 3 2 bmatrix , A^2 bmatrix 1 -1 0 bmatrix =...
- If X= bmatrix X bmatrix is a solution of the system of equations AX=B, where adj A = bmatrix 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3...
- Let |A|=6, where A is a 3 3 matrix. If | adj (3 adj (A^2. adj (2A)) ) | = 2^m 3^n, m,n N, then m+n is equal to ____.
- Let A = bmatrix 0 & 2 & -3 -2 & 0 & 1 3 & -1 & 0 bmatrix and B be a matrix such that B(I - A) = I + A. Then the sum of the...
- The number of 3 2 matrices A, which can be formed using the elements of the set -2,-1,0,1,2 such that the sum of all the diagonal...
- Let A,B and C be three 2 2 matrices with real entries such that B = (I+A)^ -1 and A+C = I. If BC = bmatrix 1 & -5 -1 & 2 bmatrix...
- Let A= bmatrix 3 & -4 1 & -1 bmatrix and B be two matrices such that A^ 100 =100B+I. Then the sum of all the elements of B^ 100...
- For a 3 3 matrix M, let trace (M) denote the sum of all the diagonal elements of M. Let A be a 3 3 matrix such that |A| = 1 2 and...
- If the system of linear equations : x + y + 2z = 6, 2x + 3y + az = a + 1, –x – 3y + bz = 2b, Where a, b R has infinitely many...
- Let A = [a_ ij ] be a 3 × 3 matrix such that A bmatrix 0 1 0 bmatrix = bmatrix 0 0 1 bmatrix , A bmatrix 4 1 3 bmatrix = bmatrix...
- If A, B and (adj(A^ -1 ) + adj(B^ -1 )) are non-singular matrices of same order, then the inverse of A(adj(A^ -1 ) + adj(B^ -1...
- If the system of equations 2x – y + z = 4 5x + λy + 3z = 12 100x – 47y + μz = 212, has infinitely many solutions, then μ – 2λ is...
- Let A be a 3 × 3 matrix such that X^T AX = O for all non-zero 3 × 1 matrices X = pmatrix x pmatrix . If A pmatrix 1 1 1 pmatrix =...
- If the system of equations x + 2y - 3z = 2 2x + + 5z = 5 14x + 3y + = 33 has infinitely many solutions, then + is equal to :
- Let M denote the set of all real matrices of order 3 × 3 and let S = –3, –2, –1, 1, 2 . Let S_1 = A = [a_ ij ] M : A = A^T and a_...
- Let A= bmatrix 1 2 & -2 0 & 1 bmatrix and P= bmatrix & - & bmatrix , θ > 0. If B=PAP^T, C=P^TB^ 10 P and the sum of the diagonal...
- Let S = m Z : A^ m^2 + A^m = 3I - A^ -6 , where A = bmatrix 2 & -1 1 & 0 bmatrix . Then n(S) is equal to …………….. .
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