Category Matrices

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’…

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively. Choose the correct answer in Exercises 22.   22. If n =…

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively. Choose the correct answer in Exercises 21. 21. The restriction on n,…

20. The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive…

19. A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to…