Sum
If A = `[(7, 3, 0),(0, 4, -2)], "B" = [(0, -2, 3),(2, 1, -4)]`, then find AT + 4BT.
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Solution
A = `[(7, 3, 0),(0, 4, -2)] "and" "B" = [(0, -2, 3),(2, 1, -4)]`
∴ AT = `[(7, 0),(3, 4),(0, -2)] "and" "B"^"T" = [(0, 2),(-2, 1),(3, -4)]`
AT + 4BT = `[(7, 0),(3, 4),(0, -2)] + 4[(0, 2),(-2, 1),(3, -4)]`
= `[(7, 0),(3, 4),(0, -2)] + [(0, 8),(-8, 4),(12, -16)]`
= `[(7 + 0, 0 + 8),(3 - 8, 4 + 4),(0 + 12, -2 - 16)]`
= `[(7, 8),(-5, 8),(12, -18)]`.
Concept: Algebra of Matrices
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