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प्रश्न
Given A = `[(1, -1),(2, 0)]`, B = `[(3, -2),(1, 1)]` and C = `[(1, 1),(2, 2)]`, find a martix X such that AXB = C
उत्तर
Given A × B × C
⇒ A–1 A × BB–1
= A–1 C B–1
I × I = A–1 CB–1
⇒ X = A–1 CB–1
Let us find A–1 and B–1
A = `[(1, -1),(2, 0)]`
|A| = 0 + 2
= 2 ≠ 0.A–1 exists
adjj A = `[(0, 1),(-2, 1)]`
∴ A–1 = `1/|"A"|` adj A = `1/2[(0, 1),(-2, 1)]`
B = `[(3, -2),(1, - 1)]`
|B| = 3 +2
= 5 ≠ 0.B–1 exists.
adj B = `[(1, 2),(-1, 3)]`
∴ B–1 = `1/|"B"|` adj B = `1/5[(1, 2),(-1, 3)]`
X = A–1 CB–1
= `2 [(0, 1),(-2, 1)] [(1, 1),(2, 2)] 1/5[(1, 2),(-1, 3)]`
= `1/10 [(0 + 2, 0 + 2),(-2 + 2, -2 + 2)][(1, 2),(-1, 3)]`
= `1/10 [(2, 2),(0, 0)] [(, 2),(-, 3)]`
= `1/10 [(2 - 2, 4 + 6),(0 - 0, 0 - 0)]`
X = `1/10[(0, 10), (0, 0)]`
= `[(0, 1),(0, 0)]`
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