Advertisements
Advertisements
Question
A = `[(3 , 1),(-1 , 2)]`, show that A2 - 5A + 7 I2 = 0.
Solution
We have
A = `[(3 , 1),(-1 , 2)]`
A = `[(3 , 1),(-1 , 2)][(3 , 1),(-1 , 2)]`
= `[(9 - 1, 3 + 2),(-3 -2, -1 + 4)]`
= `[(8, 5),(-5, 3)]`
-5A = `[((-5)·3 ,(-5)·1),((-5)·(-1),(-5)·2)]`
= `[(-5 , -5),(5 , -10)]`
7I2 = `7[(1 , 0),(0 , 1)] = [(7 , 0),(0 , 7)]`
So A2 - 5A + 712
= `[(8, 5),(-5, 3)] + [(-15 , -5),(5 , -10)]+[(7 , 0),(0 , 7)]`
= `[(8 - 15 + 7, 5 - 5 + 0),(-5 + 5 + 0, 3 - 10 + 7)] = [(0 , 0),(0 , 0)]`
So A2 - 5A + 7I2 = 0.
Hence proved.
APPEARS IN
RELATED QUESTIONS
if A = `[(2,3),(5,7)]`, B = `[(0,4),(-1,7)]` and c = `[(1,0),(-1, 4)]`, find AC + B2 – 10C.
If A = `[(2, 5),(1, 3)]`, B = `[(4, -2),(-1, 3)]` and I is the identity matric of the same order and At is the transpose of matrix A, find At.B + BI.
Evaluate:
`[(cos 45°, sin 30°),(sqrt(2) cos 0°, sin 0°)] [(sin 45°, cos 90°),(sin 90°, cot 45°)]`
If A = [4 7] and B = [3 l], find: A - B
If `|(3"a" + 2"b" , 2"a" - "b"),(4"p" - 3"q" , 2"p" + "q")|` = `|(12 , 1),(16 , 8)|` , find the values of a , b , p and q.
Find X and Y , if `|(1,2),(2 , -3)| |(x),(y)| = |(-1) , (12)|`
Given that A = `[(3, 0),(0, 4)]` and B = `[(a, b),(0, c)]` and that AB = A + B, find the values of a, b and c.
If B = `[(-4, 2),(5, -1)] and "C" = [(17, -1),(47, -13)]` find the matrix A such that AB = C
If A = `[(3/5, 2/5),(x, y)]` and A2 = I, find x,y
Find a and b if `[(a - b, b - 4),(b + 4, a - 2)] [(2, 0),(0, 2)] = [(2, -2),(14, 0)]`
