Show that ` A=[[-8,5],[2,4]]` satifies the equation ` A^2 +4A-42=0 `

Show that A=[(-8, 5),( 2, 4)] satisfies the equation A^2+4A-42 I=O . Hence, find A^(-1) .

Show that the matrix A=[2 3 1 2] satisfies the equation A^2-4A+I=0

Show that the matrix A=[[1,2,2],[2,1,2],[2,2,1]] satisfies the equation A^2-4A-5I_3=0 and hence find A^(-1)

Solve the equation x^4-5x^2+4=0 .

Pick out the solution from the values given in the bracket next to each equation. Show that the other values do not satisfy the equation. (a) 5 = 60 (10 , 5, 12, 15) (b) n + 12 = 20 (12, 8, 20, 0) (c) p - 5 = 5 (0, 10, 5 - 5) (d) q/2 = 7 (7, 2, 10, 14) (e) r - 4 = 0 (4, -4.8.0) (f) x + 4 = 2 (- 2, 0, 2, 4)

If A=[[1,2],[4,2]] , then show that |2A|=4|A|

Solve the equation 4^(x)- 5 xx2^(x) + 4 = 0.

Show that the equation 3x^(2)+4y^(2)-12x-8y+4=0 represents an ellipse. Find the focus also

The value of alpha in [0,2pi] which does not satify the equation int_(pi//2)^(alpha) sin x dx = sin 2 alpha, is