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Matrices

Question

Construct a 3 x 3 matrix w'hose elements are giv en by a,1, = 2 i – 3 j

Solution

Let A = [a i] be required 3 x3 matrix
where a,ij , = 2 i – 3 j
∴ a₁₁, = 2–3 = –1. a₁₂ = 2–6 = 4. a₁₃,= 2–9 = 7
a₂₁ = 4 — 3 = 1. a₂₂ = 4 — 6 = —2 . a₂₃ = 4 –9 = 5
a₃₁ = 6 – 3 = 3, = 6 – 6 = 0 , a₃₃ = 6 – 9 = –3
$therefore space space space space space straight A equals open square brackets table row cell negative 1 end cell cell negative 4 end cell cell negative 7 end cell row 1 cell negative 2 end cell cell negative 5 end cell row 3 0 cell negative 3 end cell end table close square brackets$

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Matrices

Construct a 3 x 3 matrix w'hose elements are giv en by a,1, = 2 i – 3 j

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