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…
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…
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 &…
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 \…
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 \…
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 &…
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.…
11. If (xbegin{bmatrix}2 \ 3 end{bmatrix})+(ybegin{bmatrix}-1 \ 1 end{bmatrix})=(begin{bmatrix}10 \ 5 end{bmatrix}), find the values of x and y. Previous Next Matrices Exercise 3.2 1. Let (A=begin{bmatrix}2 & 4 \ 3 & 2 end{bmatrix}), (B=begin{bmatrix}1 & 3 \ -2 &…
10. Solve the equation for x, y, z and t, if 2(begin{bmatrix}x & z \ y & t end{bmatrix})+3(begin{bmatrix}1 & -1 \ 0 & 2 end{bmatrix})=3(begin{bmatrix}3 & 5 \ 4 & 6 end{bmatrix}) Previous Next Matrices Exercise 3.2 1. Let…
9. Find x and y, if 2(begin{bmatrix}1 & 3 \ 0 & x end{bmatrix}) + (begin{bmatrix}y & 0 \ 1 & 2 end{bmatrix})=(begin{bmatrix}5 & 6 \ 1 & 8 end{bmatrix}) Previous Next Matrices Exercise 3.2 1. Let (A=begin{bmatrix}2 &…
