Algebra of Matrices: JEE Questions & Solutions

For the matrices A = bmatrix 3 & -4 1 & -1 bmatrix and B = bmatrix -29 & 49 -13 & 18 bmatrix, if (A^15 + B) bmatrix x y bmatrix = bmatrix 0…

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 diagonal…

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 elements…

Let A = [aij] be a 3 3 matrix such that: A = bmatrix 0 & 0 & 4 1 & 0 & 0 0 & 1 & 3 bmatrix, A^-1 = bmatrix 0 & 1 & 0 1 & 3 & 0 2 & 1 & 0…

Let A = [ arraycc 1 2 & -2 0 & 1 array ] and P = [ arraycc & - & array ], 0. If B = P A P^T, C = P^T B 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:

Let A = [aij] be a matrix of order 3 3, with aij = ( 2)^i+j. If the sum of all the elements in the third row of A^2 is + 2, where, Z, then…

Let A = bmatrix & -1 6 & bmatrix, 0, such that (A) = 0 and + = 1. If I denotes the 2 2 identity matrix, then the matrix (I + A)^5 is:

Let A be a 3 3 real matrix such that A^2(A - 2I) - 4(A - I) = O, where I and O are the identity and null matrices, respectively. If A^3 =…

Let A = bmatrix & 0 & - 0 & 1 & 0 & 0 & bmatrix. If for some (0,), A^2 = A^T, then the sum of the diagonal elements of the matrix ((A +…

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Given f(x)= bmatrix x & - x & 0 x & x & 0 0 & 0 & 1 bmatrix Evaluate: Statement I: f(-x) is the inverse of f(x). Statement II: f(x)…

Let be a 2 2 real matrix and I be the identity matrix of order 2. If the roots of the equation | - xI| = 0 are -1 and 3, then the sum of…

Let A be a square matrix such that AA^T = I. Then 12A[(A + A^T)^2 + (A - A^T)^2] is equal to:

Let R = diag(, ( + 2 /3), ( + 4 /3)) be a diagonal 3 3 matrix. For a square matrix M, let trace(M) denote the sum of all the diagonal…

Let and be real numbers. Consider a 3 3 matrix A such that: A^2 = 3A + I, A^4 = 21A + I. Then:

Let A be a symmetric matrix such that |A| = 2 and bmatrix 3 & -2 2 & 1 bmatrix A = bmatrix 1 & 2 2 & 7 bmatrix. If the sum of the diagonal…

Let A = pmatrix 1 & 0 & 0 0 & 4 & -1 0 & 12 & -3 pmatrix Then the sum of the diagonal elements of the matrix (A + I)^11 is equal to:

If A = 12 bmatrix 1 & 3 - 3 & 1 bmatrix, then:

Let A = [aij]2 2, where aij 0 for all i, j, and A^2 = I. Let a be the sum of all diagonal elements of A and b = |A|. Then 3a^2 + 4b^2 is…

Let P be a square matrix such that P^2 = I - P. For,,, N, if P + P = I - 29P and P - P = I - 13P, then + + - is equal to:

Let P = bmatrix 32 & 12 - 12 & 32 bmatrix, A = bmatrix 1 & 1 0 & 1 bmatrix, and Q = PAP^T. If P^TQ^2007P = bmatrix a & b c & d bmatrix,…

Let A be a 2 2 matrix with real entries such that A^T = A + I, where R -1, 1. If (A^2 - A) = 4, then the sum of all possible values of is…

Let A = bmatrix 0 & 1 & 2 1 & 0 & 3 1 & 0 & 0 bmatrix, where a, c R. If A^n = A and the positive value of a belongs to the interval (n-1,…

Let A = bmatrix 1 & 151 0 & 1 bmatrix. If B = bmatrix 1 & 2 -1 & -1 bmatrix A bmatrix -1 & -2 1 & 1 bmatrix, then the sum of all the…