5. If (A=begin{bmatrix}3&1 \ -1&2end{bmatrix}), show that (A^2-5A+7I=0). Previous Next Class 12 Matrices Miscellaneous Exercise 1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix. 2. Show that the matrix B’AB is symmetric or…
4. For what values of x: (A=begin{bmatrix}1&2&1end{bmatrix}) (begin{bmatrix}1&2&0 \2&0&1\1&0&2 end{bmatrix})(begin{bmatrix}0\2\x end{bmatrix}=O?) Previous Next Class 12 Matrices Miscellaneous Exercise 1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix. 2. Show that the matrix B’AB…
3. Find the values of x, y, z if the matrix (A=begin{bmatrix}0 & 2y & z \ x & y & -z \ x & -y & z end{bmatrix}) satisfy the equation (A’A=I). Previous Next Class 12 Matrices Miscellaneous Exercise…
2. Show that the matrix B’AB is symmetric or skew symmetric according as A is symmetric or skew symmetric. Previous Next Class 12 Matrices Miscellaneous Exercise 1. If A and B are symmetric matrices, prove that AB–BA is a skew…
1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix. Previous Next Class 12 Matrices Miscellaneous Exercise 1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix. 2.…
12. If (A=begin{bmatrix}cosα & -sinα \ sinα & cosα end{bmatrix}), then A+A’=I, if the value of α is: (A) (pi over 6) (B) (pi over 3) (C) (pi) (D) ({3pi over 2}) Previous Next Class 12 Matrices Exercise 3.3 1.…
11. If A, B are symmetric matrices of same order, then AB – BA is a (A) Skew symmetric matrix(B) Symmetric matrix(C) Zero matrix(D) Identity matrix Previous Next Class 12 Matrices Exercise 3.3 1. Find the transpose of each of…
10. Express the following matrices as the sum of a symmetric and a skew symmetricmatrix: (i) (begin{bmatrix}3 & 5 \ 1 & -1 end{bmatrix}) (ii) (begin{bmatrix}6 & -2 & 2 \ -2 & 3 & -1 \ 2 & -1…
9. Find ({1over 2}(A+A’)) and ({1over 2}(A-A’)), when (A=begin{bmatrix}0 & a & b \ -a & 0 & c \ -b & -c & 0 end{bmatrix}). Previous Next Class 12 Matrices Exercise 3.3 1. Find the transpose of each of…
8. For the matrix (A=begin{bmatrix}1 & 5 \ 6 & 7 end{bmatrix}), verify that (i) (A+A’) is a symmetric matrix (ii) (A-A’) is a skew symmetric matrix. Previous Next Class 12 Matrices Exercise 3.3 1. Find the transpose of each…
