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Evaluate the following expression: [tex]\(5(1,3) - 3(2,-1)\)[/tex].

A. [tex]\((11,0)\)[/tex]
B. [tex]\((-3,-2)\)[/tex]
C. [tex]\((11,3)\)[/tex]
D. [tex]\((-1,18)\)[/tex]

Sagot :

GinnyAnswer
To evaluate the expression [tex]\(5(1,3) - 3(2,-1)\)[/tex], follow these detailed steps:

1. Scale the first vector: Multiply the vector [tex]\((1,3)\)[/tex] by 5.
[tex]\[ 5(1,3) = (5 \cdot 1, 5 \cdot 3) = (5, 15) \][/tex]

2. Scale the second vector: Multiply the vector [tex]\((2,-1)\)[/tex] by -3.
[tex]\[ -3(2,-1) = (-3 \cdot 2, -3 \cdot -1) = (-6, 3) \][/tex]

3. Add the scaled vectors: Add the results of the scaled vectors from steps 1 and 2.
[tex]\[ (5, 15) + (-6, 3) = (5 + (-6), 15 + 3) = (-1, 18) \][/tex]

Therefore, the evaluated expression [tex]\(5(1,3) - 3(2,-1)\)[/tex] is [tex]\((-1, 18)\)[/tex].

So, the answer is:
D. [tex]\((-1, 18)\)[/tex]
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