Advertisements
Advertisements
प्रश्न
A = `[(1, 0),(2, 1)] and "B" = [(2, 3),(-1, 0)]` Find A2 + AB + B2
उत्तर
Given that
A = `[(1, 0),(2, 1)]`
B = `[(2, 3),(-1, 0)]`
A2 = A x A = `[(1, 0),(2, 1)] xx [(1, 0),(2, 1)]`
= `[(1 xx 1 + 0 xx 2, 1 xx 0 + 0 xx 1),(2 xx 1 + 1 xx 2, 2 xx 0 + 1 xx 1)]`
= `[(1 + 0, 0 + 0),(2+ 2, 0+ 1)]`
= `[(1, 0),(4, 1)]`
A x B = `[(1, 0),(2, 1)] xx [(2, 3),(-1, 0)]`
= `[(1 xx 2 + 0 xx -1 , 1 xx 3 + 0 xx 0),(2 xx 2 + 1 xx 1, 2 xx 3 + 1 xx 0)]`
= `[(2, 3),(3, 6)]`
B2 = B x B = `[(2, 3),(-1, 0)] xx [(2, 3),(-1, 0)]`
= `[(2 xx 2 + 3 xx (-1), 2 xx 3 + 3 xx 0),(-1 xx 2 + 0 xx (-1), -1 xx 3 + 0 xx 0)]`
= `[(4 - 3, 6 + 0),(-2 + 0, -3 + 0)]`
= `[(1, 6),(-2, -3)]`
A2 + AB + B2 = `[(1, 0),(4, 1)] + [(2, 3),(3, 6)] + [(1, 6),(-2, -3)]`
= `[(1 + 2 + 1, 0 + 3 + 6),(4 + 3 - 2, 1 + 6 + -3)]`
= `[(4, 9),(5, 4)]`.
APPEARS IN
संबंधित प्रश्न
In the given case below find
a) The order of matrix M.
b) The matrix M
`M xx [(1,1),(0, 2)] = [1, 2]`
If `P = [(2,6),(3,9)]` and `Q = [(3,x),(y, 2)]` find x and y such that PQ = null matrix
Find the matrix A, If B =`[(2,1),(0,1)] and B^2 = B+1/2A`
If A = `[(3, 5),(4, -2)] and "B" = [(2),(4)]` , is the product AB possible ? Give a reason. If yes, find AB.
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. A + CB
If `[(1, 2),(3, 3)] [(x, 0),(0, y)] = [(x, 0),(9, 0)]`find the values of x and y
Find the value of x given that A2 = B Where A = `[(2, 12),(0, 1)] and "B" = [(4, x),(0, 1)]`
Choose the correct answer from the given four options :
If A = `[(0, 1),(1, 0)]`, then A2 =
Choose the correct answer from the given four options :
If A = `[(0, 0),(1, 0)]`, then A2 =
If A = `[(3, 2),(0, 5)] and "B" = [(1, 0),(1, 2)]` find the each of the following and state it they are equal: (A + B)(A – B)
