Advertisements
Advertisements
Question
If M = `[(4,1),(-1,2)]`, show that 6M – M2 = 9I; where I is a 2 × 2 unit matrix.
Solution
M2 = `[(4, 1),(-1, 2)][(4, 1),(-1, 2)]`
= `[(4 xx 4 + 1 xx (-1), 4 xx 1 + 1 xx 2),(-1 xx 4 + 2 xx (-1), -1 xx 1 + 2 xx 2)]`
= `[(16 - 1,4 + 2),(-4 - 2, -1 + 4)]`
= `[(15, 6),(-6, 3)]`
6M – M2 = `6[(4, 1),(-1, 2)] - [(15, 6),(-6, 3)]`
= `[(24, 6),(-6,12)] - [(15,6),(-6,3)]`
= `[(24 - 15, 6 - 6),(-6 - (-6), 12 - 3)]`
= `[(9, 0),(0, 9)]`
= `9[(1, 0),(0, 1)]`
= 9I
Hence proved.
APPEARS IN
RELATED QUESTIONS
Given A = `[(0, 4, 6),(3, 0, -1)]` and B = `[(0, 1),(-1, 2),(-5, -6)]`, find if possible BA
Given A = `[(4, 1),(2, 3)]` and B = `[(1, 0),(-2, 1)]`, find AB.
If A = `[(3, 5),(4,- 2)]` and B = `[(2),(4)]`, is the product AB possible ? Given a reason. If yes, find AB.
If A = `[(1, 2),(2, 1)] and "B" = [(2, 1),(1, 2)]`, fin A(BA)
Given martices A = `[(2, 1),(4, 2)] and "B" = [(3, 4),(-1, -2)], "C" = [(-3, 1),(0, -2)]` Find the products of (i) ABC (ii) ACB and state whether they are equal.
A = `[(1, 0),(2, 1)] and "B" = [(2, 3),(-1, 0)]` Find A2 + AB + B2
If A = `[(1, 1),(x, x)]`,find the value of x, so that A2 – 0
Find x and y if `[(-3, 2),(0, -5)] [(x),(2)] = [(5),(y)]`
If P = `[(2, 6),(3, 9)]` and Q = `[(3, x),(y, 2)]`, find x and y such that PQ = null matrix.
Choose the correct answer from the given four options :
A = `[(1, 0),(0, 1)]` then A2 =
