Matrices questions
472 published questions with worked solutions.
- Let S_1 and S_2 be respectively the sets of a – 0 for which the system of linear equations ax + 2ay – 3az = 1, (2a+1)x + (2a+3)y...
- Let x, y, z > 1 and A = bmatrix 1& _xy& _xz _yx&2& _yz _zx& _zy&3 bmatrix . Then |adj(adjA^2)| is equal to
- The set of all value of t R, for which the matrix bmatrix e^t&e^ -t ( t-2 t)&e^ -t (-2 t- t) ^t&e^ -t (2 t+ t)&e^ -t ( t-2 t)...
- Let and be real numbers. Consider a 3 × 3 matrix A such that A^2=3A+ I. If A^4=21A+ I, then
- Consider the following system of equations + 2y + z = 1, 2 + 3y + z = 1, 3x + + 2z = For some , R when which of the following is...
- If P is a 3 × 3 real matrix such that P^T = aP + (a – 1)I, where a > 1, then
- Let A = pmatrix m&n &q pmatrix , d = |A| 0 and |A – d(AdjA)| = 0. Then
- Let the system of linear equations x + y + kz = 2, 2x + 3y – z = 1, 3x + 4y + 2z = k have infinitely many solutions. Then the...
- Let A be a n × n matrix such that |A| = 2. If the determinant of the matrix Adj(2 (2A^ -1 )) is 2^ 84 , then n is equal...
- 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 :
- Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations: 3x - y - z = 0 -3x + z = 0 -3x +...
- Consider the matrix P = pmatrix 2 & 0 & 0 0 & 2 & 0 0 & 0 & 3 pmatrix . Let the transpose of a matrix X be denoted by X^T. Then...
- If A = bmatrix a & b & a bmatrix and A^2 = bmatrix & & bmatrix , then
- Let A = pmatrix 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 pmatrix (10)B = pmatrix 4 & 2 & 2 -5 & 0 & 1 & -2 & 3 pmatrix . If B
- If A^2 - A + I = 0, then the inverse of A is
- If A and B are square matrices of size n n such that A^2 - B^2 = (A - B)(A + B), then which of the following will be always true?
- Let A = pmatrix 1 & 2 3 & 4 pmatrix and B = pmatrix a & 0 0 & b pmatrix , a, b N. Then
- Let A be a 2 2 matrix with real entries. Let I be the 2 2 identity matrix. Denote by tr(A), the sum of diagonal entries of A....
- Let A be a square matrix all of whose entries are integers. Then which one of the following is true?
- Let A be a 2 × 2 matrix Statement-1 : adj(adj A) = A Statement-2 : |adj A| = |A|
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