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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…

7. (i) Show that the matrix (A=begin{bmatrix}1 & -1 & 5 \ -1 & 2 & 1\5 & 1 & 3 end{bmatrix}) is a symmetric matrix. (ii) Show that the matrix (A=begin{bmatrix}0 & 1 & -1 \ -1 & 0…

6. (i) If (A=begin{bmatrix}cosα & sinα \ -sinα & cosα end{bmatrix}), then verify that A’A=I. (ii) If (A=begin{bmatrix}sinα & cosα \ -cosα & sinα end{bmatrix}), then verify that A’A=I. Previous Next Class 12 Matrices Exercise 3.3 1. Find the transpose…

5. For the matrices A and B, verify that (AB)′ = B′A′, where  (i) (A=begin{bmatrix}1 \ -4 \ 3 end{bmatrix}), (B=begin{bmatrix}-1 & 2 & 1end{bmatrix}) (ii) (A=begin{bmatrix}0 \ 1 \ 2 end{bmatrix}), (B=begin{bmatrix}1 & 5 & 7end{bmatrix})  Previous Next Class…

4. If (A’=begin{bmatrix}-2 & 3 \ 1 & 2 end{bmatrix}) and (B=begin{bmatrix}-1 & 0 \ 1 & 2 end{bmatrix}), then find (A+2B)’. Previous Next Class 12 Matrices Exercise 3.3 1. Find the transpose of each of the following matrices: (i)…

3. If (A’=begin{bmatrix}3 & 4 \ -1 & 2 \0 & 1end{bmatrix}) and (B=begin{bmatrix}-1 & 2 & 1 \ 1 & 2 & 3 end{bmatrix}), then verify that (i) (A+B)’=A’+B’ (ii) (A-B)’=A’-B’ Previous Next Class 12 Matrices Exercise 3.3 1.…

2. If  (A=begin{bmatrix}-1 & 2 & 3 \ 5 & 7 & 9 \-2 & 1 & 1end{bmatrix}) and (B=begin{bmatrix}-4 & 1 & -5 \ 1 & 2 & 0 \1 & 3 & 1end{bmatrix}), then verify that  (i) (A+B)’=A’+B’…