Vector and Arithmetic Sequences Problem Solutions

9)
Answer:
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A = [−5 2] & B = [1 0]
Vector multiplication property:
X = [xi1]
is a row vector, and α be any scalar, then:
α · X = [α · xi1]
Therefore,
3A = 3[−5 2] = [3 × −5 3 × 2] = [−15 6]
4B = 4[1 0] = [4 × 1 4 × 0] = [4 0]
Vector addition property:
X = [xi1] &Y = [yi1]
be two row vectors. Then:
X + Y = [xi1 + yi1]
Therefore,
3A + 4B = [−15 6] + [4 0] = [−15 + 4 6 + 0] = [−11 6]
10)
Answer :
Let a t-shirt sell for t$ and a banner for b$.
Justine sells 13 t-shirts and 10 banners for 145$. Implies,
13t + 10b = 145 (1)
Carlos sells 15 t-shirts and 6 banners for 141$. Implies,
15t + 6b = 141 (2)
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