Matrices questions
472 published questions with worked solutions.
- Let the system of linear equations x + y + z = 2, 3x + y + z = 4, x + 2z = 1 have a unique solution (x*, y*, z*). If ( , x*),...
- Let A = bmatrix 2 & -2 1 & -1 bmatrix and B = bmatrix -2 & 2 -1 & 1 bmatrix , Then the number of elements in the set (n, m) : n,...
- Let A be a 3 3 real matrix such that A(1, 1, 0)ᵀ = (1, 1, 0)ᵀ, A(1, 0, 1)ᵀ = (−1, 0, 1)ᵀ and A(0, 0, 1)ᵀ = (1, 1, 2)ᵀ. If X = (x_...
- Let A = bmatrix 0 & -2 2 & 0 bmatrix . If M and N are two matrices given by M = _ k=1 ^ 10 A^ 2k and N = _ k=1 ^ 10 A^ 2k-1 then...
- Let A = bmatrix 1 1 1 bmatrix and B = bmatrix 9^ 2 & -10^ 2 & 11^ 2 12^ 2 & 13^ 2 & -14^ 2 -15^ 2 & 16^ 2 & 17^ 2 bmatrix , then...
- The number of matrices A = bmatrix a & b c & d bmatrix , where a, b, c, d −1, 0, 1, 2, 3, _____, 10 , such that A = A^ -1 , is...
- Let A be a 2 2 matrix with det(A) = −1 and det((A + I)(Adj(A) + I)) = 4. Then the sum of the diagonal elements of A can be
- If the system of equations x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = has infinitely many solutions, then the ordered pair ( ,...
- Let A be a 3 3 invertible matrix. If |adj(24A)| = |adj(3 adj(2A))|, then |A|^ 2 is equal to :
- The number of elements in the set A= pmatrix a&b 0&d pmatrix :a,b,d -1,0,l and (I-A)^3=I-A^3 , where I is 2 × 2 identity matrix ,...
- If A = 1 2 bmatrix 1& 3 - 3&1 bmatrix , then :
- 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
- For the system of equations x + y + z = 6, x + 2y + = 10, x + 3y + 5z = , which one of the following is NOT true?
- The number of 3 3 matrices A whose entries are either 0 or 1 and for which the system A bmatrix x bmatrix = bmatrix 1 0 0 bmatrix...
- Let k be a positive real number and let A = bmatrix 2k-1 & 2 k & 2 k 2 k & 1 & -2k -2 k & 2k & -1 bmatrix and B = bmatrix 0 &...
- Let M and N be two 3×3 non-singular skew-symmetric matrices such that MN = NM. If P^T denotes the transpose of P, then M^2N^2...
- Let M be a 3×3 matrix satisfying M bmatrix 0 1 0 bmatrix = bmatrix -1 2 3 bmatrix , M bmatrix 1 -1 0 bmatrix = bmatrix 1 1 -1...
- If P is a 3 × 3 matrix such that P^T = 2P + I, where P^T is the transpose of P and I is the 3 × 3 identity matrix, then there...
- If the adjoint of a 3×3 matrix P is bmatrix 1 & 4 & 4 2 & 1 & 7 1 & 1 & 3 bmatrix , then the possible value(s) of the determinant...
- For 3 × 3 matrices M and N, which of the following statement(s) is (are) **NOT** correct ?
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