Advertisements
Advertisements
प्रश्न
If X = `[(4, 1),(-1, 2)]`,show that 6X – X² = 9I Where I is the unit matrix.
उत्तर
X = `[(4, 1),(-1, 2)]`
x2 = x × x = `[(4, 1),(-1, 2)][(4, 1),(-1, 2)]`
= `[(16 - 1, 4 + 2),(-4 -2 , -1 + 4)]`
= `[(15, 6),(-6, 3)]`
L.H.S. 6X – x2 = `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)]`
= 91
= R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find x and y, if `[(x, 0),(-3, 1)][(1, 1),(0, y)] = [(2, 2),(-3, -2)]`
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.
Given the matrices:
A = `[(2, 1),(4, 2)]`, B = `[(3, 4),(-1, -2)]` and C = `[(-3, 1),(0, -2)]`. Find:
- ABC
- ACB.
State whether ABC = ACB.
Evaluate without using tables:
`[(2cos 60°, -2sin 30°),(-tan45°, cos 0°)] [(cos 45°, cosec 30°),(sec 60°, sin 90°)]`
If A = `[(3, 5),(4,- 2)]` and B = `[(2),(4)]`, is the product AB possible ? Given a reason. If yes, find AB.
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, 2),(3, 4)] and "B" = [(6, 1),(1, 1)], "C" = [(-2, -3),(0, 1)]` find each of the following and state if they are equal.CA + B
If A = `[(2, 1),(0, -2)] and "B" = [(4, 1),(-3, -2)], "C" = [(-3, 2),(-1, 4)]` Find A2 + AC – 5B
Find the matrix X of order 2 × 2 which satisfies the equation `[(3, 7),(2, 4)] [(0, 2),(5, 3)] + 2"X" = [(1, -5),(-4, 6)]`
If `[(3, 4),(5, 5)] = [(a, b),(c, d)] [(1, 0),(0, 1)]`write down the values of a,b,c and d
