Matrices questions
472 published questions with worked solutions.
- The third element in the second row of adjoint of a matrix A = [a_ ij ]_ 3 3 (where a_ ij = 2i + j) is
- If matrix A = 1 11 bmatrix -1&7&-24 2&a&4 2&-3&15 bmatrix and A^ -1 = bmatrix 3&3&4 2&-3&4 &-1&c bmatrix , then the values of a,...
- If A= bmatrix 1& 2 - 2 &1 bmatrix then A^ -1 =
- If A= bmatrix 1&-1&1 0&2&-3 2&1&0 bmatrix , B= adj A and C=5A, then | adj B| |C| =
- If A and B are non-singular matrices of order 2 such that (AB)^ -1 = 16 bmatrix -7&-3 2&3 bmatrix and A^ -1 = 13 bmatrix 4&3 -1&0...
- If A = bmatrix 5a & -b 3 & 2 bmatrix and A adj A = AA^T, then 5a + b =
- If A= bmatrix 3&-3&4 2&-3&4 0&-1&1 bmatrix _ 3 3 , then A^ -1 =
- If A is a matrix of order 2 and I is the identity matrix of order such that A^2 - 4A + 3I = 0 then (A + 3I)^ -1 =
- If A= bmatrix 1&-2&2 0&2&-3 3&-2&4 bmatrix then A(I+ adj A)=
- If A = pmatrix - 1 0 0 pmatrix , B = pmatrix + 1 0 0 pmatrix be two matrices, then AB^T is a non-zero matrix for |α| not equal to
- If the system of equations x + y + z = 6 x + 2y + 3z = 10 x + 2y + z = 0 has a unique solution, then λ is not equal to
- Let A and B be real matrices of the form bmatrix & 0 0 & bmatrix and bmatrix 0 & & 0 bmatrix , respectively. Statement 1: AB − BA...
- If A^T denotes the transpose of the matrix A = bmatrix 0 & 0 & a 0 & b & c & e & f bmatrix , where a, b, c, d, e and f are...
- If A = bmatrix 1 & 0 & 0 2 & 1 & 0 -3 & 2 & 1 bmatrix and B = bmatrix 1 & 0 & 0 -2 & 1 & 0 7 & -2 & 1 bmatrix then AB equals
- Let A = pmatrix 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 pmatrix . If u_1 and u_2 are column matrices such that Au_1 = pmatrix 1 0 0 pmatrix...
- The matrix A^2 + 4A - 5I, where I is identity matrix and A = bmatrix 1 & 2 4 & -3 bmatrix , equals :
- If p, q, r are 3 real numbers satisfying the matrix equation, [p q r] bmatrix 3 & 4 & 1 3 & 2 & 3 2 & 0 & 2 bmatrix = [3 0 1]...
- If the system of linear equations : x_1 + 2x_2 + 3x_3 = 6 x_1 + 3x_2 + 5x_3 = 9 2x_1 + 5x_2 + ax_3 = b is consistent and has...
- Let A, other than I or −I, be a 2 × 2 real matrix such that A^2 = I, I being the unit matrix. Let Tr(A) be the sum of diagonal...
- If B is a 3 3 matrix such that B^2 = 0, then [(I + B)^ 50 - 50B ] is equal to :
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