Advertisements
Advertisements
प्रश्न
If A = `[(2, 1),(0, 0)]`, B = `[(2, 3),(4, 1)]` and C = `[(1, 4),(0, 2)]`; then show that A(B + C) = AB + AC.
उत्तर
B + C = `[(2, 3),(4, 1)] + [(1, 4),(0, 2)] = [(3, 7),(4, 3)]`
A(B + C) = `[(2, 1),(0, 0)][(3, 7),(4, 3)]`
= `[(6 + 4, 14 + 3),(0 ,0)]`
= `[(10, 17),(0 ,0)]`
AB = `[(2, 1),(0, 0)][(2, 3),(4, 1)]`
= `[(4 + 4, 6 + 1),(0, 0)]`
= `[(8, 7),(0, 0)]`
AC = `[(2, 1),(0, 0)][(1, 4),(0, 2)]`
= `[(2 + 0, 8 + 2),(0, 0)]`
= `[(2, 10),(0, 0)]`
AB + AC = `[(8, 7),(0, 0)] + [(2, 10),(0, 0)]`
= `[(10, 17),(0, 0)]`
Hence, A(B + C) = AB + AC
APPEARS IN
संबंधित प्रश्न
Find x and y if `3[(4, x)] + 2[(y, -3)] = [(10, 0)]`
If `[(4, -2),(4, 0)] + 3A = [(-2, -2),(1, -3)]`; find A.
If `2[(3, x),(0, 1)] + 3[(1, 3),(y, 2)] = [(z, -7),(15, 8)]`; find the values of x, y and z.
Given A = `[(-3, 6),(0, -9)]` and At is its transpose matrix. Find 2At – 3A
If A = `[(0, 2),(5, -2)]`, B = `[(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find B2A
If A = `|(15,7),(13,8)|` and B = `|(16 , 12),(27,11)|` , find matrix X such that A + X
Given A = `[(1, 4),(2, 3)]` and B = `[(-4, -1),(-3, -2)]` find the matrix 2A + B
If A = `[(2, a),(-3, 5)] and "B" = [(-2, 3),(7, b)], "C" = [(c, 9),(-1, -11)]` and 5A + 2B = C, find the values of a,b,c
Find X if Y = `[(3, 2),(1, 4)]` and 2X + Y = `[(1, 0),(-3, 2)]`
If I is a unit matrix of order 2 and M + 4I = `[(8, -3),(4, 2)]`, the matrix M is ______.
