Advertisements
Advertisements
प्रश्न
If M = `[(1, 2),(2, 1)]` and I is a unit matrix of the same order as that of M; show that: M2 = 2M + 3I.
उत्तर
M2 = `[(1, 2),(2, 1)][(1, 2),(2, 1)]`
= `[(1 xx 1 + 2 xx 2, 1 xx 2 + 2 xx 1),(2 xx 1 + 1 xx 2, 2 xx 2 + 1 xx 1)]`
= `[(1 + 4, 2 + 2),(2 + 2, 4 + 1)]`
= `[(5, 4),(4, 5)]`
2M + 3I = `2[(1, 2),(2, 1)] + 3[(1, 0),(0, 1)]`
= `[(2, 4),(4, 2)] + [(3, 0),(0, 3)]`
= `[(5, 4),(4, 5)]`
Hence, M2 = 2M + 3I
APPEARS IN
संबंधित प्रश्न
if `A = [(3,5),(4,-2)] and B = [(2),(4)]`is the product AB possible? Give a reason. If yes, find AB
Given A = `[(4, 1),(2, 3)]` and B = `[(1, 0),(-2, 1)]`, find AB.
If M = `[(4,1),(-1,2)]`, show that 6M – M2 = 9I; where I is a 2 × 2 unit matrix.
Construct a 2 x 2 matrix whose elements aij are given by
aij = 2i - j
Given A = `[(1, 1),(8, 3)]`, evaluate A2 – 4A
If A = `[(1, 2),(2, 3)] and "B" = [(2, 1),(3, 2)], "C" = [(1, 3),(3, 1)]` find the matrix C(B – A)
Show that `[(1, 2),(2, 1)]` is a solution of the matrix equation X² – 2X – 3I = 0,Where I is the unit matrix of order 2
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 A = `[(3, x),(0, 1)] and "B" = [(9, 16),(0, -y)]`find x and y when A2 = B
