The restriction on n, k and p so that PY + WY will be defined are:
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,…
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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
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…
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
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…
If (A=\begin{bmatrix}0 & -tan{α\over 2} \ tan{α\over 2 and I is the identity matrix of order 2, show that I+A=(I-A)
18. If (A=begin{bmatrix}0 & -tan{αover 2} \ tan{αover 2} & 0end{bmatrix}) and I is the identity matrix of order 2, show that I+A=(I-A)(begin{bmatrix}cosα & -sinα \ sinα & cosαend{bmatrix}). Previous Next Matrices Exercise 3.2 1. Let (A=begin{bmatrix}2 & 4…
If (A=\begin{bmatrix}3 & -2 \ 4 & -2 find k so that (A^2=kA-2I).If (A=\begin{bmatrix}3 & -2 \ 4 & -2
17. If (A=begin{bmatrix}3 & -2 \ 4 & -2end{bmatrix}) and (I=begin{bmatrix}1 & 0 \ 0 & 1end{bmatrix}), find k so that (A^2=kA-2I). Previous Next Matrices Exercise 3.2 1. Let (A=begin{bmatrix}2 & 4 \ 3 & 2 end{bmatrix}), (B=begin{bmatrix}1 & 3…
If (A=\begin{bmatrix}1 & 0 & 2 \ 0 & 2 & 1 \ 2 & 0 & 3 prove that (A^3-6A^2+7A+2I=0)
16. If (A=begin{bmatrix}1 & 0 & 2 \ 0 & 2 & 1 \ 2 & 0 & 3end{bmatrix}), prove that (A^3-6A^2+7A+2I=0) Previous Next Matrices Exercise 3.2 1. Let (A=begin{bmatrix}2 & 4 \ 3 & 2 end{bmatrix}), (B=begin{bmatrix}1 &…
Find (A^2-5A+6I), if (A=\begin{bmatrix}2 & 0 & 1 \ 2 & 1 & 3
15. Find (A^2-5A+6I), if (A=begin{bmatrix}2 & 0 & 1 \ 2 & 1 & 3 \ 1 & -1 & 0end{bmatrix}) Previous Next Matrices Exercise 3.2 1. Let (A=begin{bmatrix}2 & 4 \ 3 & 2 end{bmatrix}), (B=begin{bmatrix}1 & 3 \…
Show that (i) (\begin{bmatrix}5 & -1 \ 6 & 7 \end{bmatrix})(\begin{bmatrix}2 & 1 \ 3
14. Show that (i) (begin{bmatrix}5 & -1 \ 6 & 7 end{bmatrix})(begin{bmatrix}2 & 1 \ 3 & 4 end{bmatrix})≠(begin{bmatrix}2 & 1 \ 3 & 4 end{bmatrix})(begin{bmatrix}5 & -1 \ 6 & 7 end{bmatrix}) (ii) (begin{bmatrix}1 & 2 & 3 \…
If (F(x)=\begin{bmatrix}cosx & -sinx & 0 \ sinx & cosx & 0 \ 0 & 0 & 1 \end{bmatrix}), show that (F(x)F(y)=F(x+y)).
13. If (F(x)=begin{bmatrix}cosx & -sinx & 0 \ sinx & cosx & 0 \ 0 & 0 & 1 end{bmatrix}), show that (F(x)F(y)=F(x+y)). Previous Next Matrices Exercise 3.2 1. Let (A=begin{bmatrix}2 & 4 \ 3 & 2 end{bmatrix}), (B=begin{bmatrix}1 &…
Given 3(\begin{bmatrix}x & y \ z & w find the values of x, y, z and w.Given 3(\begin{bmatrix}x & y \ z & w
12. Given 3(begin{bmatrix}x & y \ z & w end{bmatrix})=(begin{bmatrix}x & 6 \ -1 & w end{bmatrix})+(begin{bmatrix}4 & x+y \ z+w & 3 end{bmatrix}), find the values of x, y, z and w. Previous Next Matrices Exercise 3.2 1.…