Given vectors a = [3, 2] and b = [4, 2], find the column vector p = 5a - 2b.

April 24, 2026Mathematics

ScanSolve AI Answer

April 24, 2026

Answer

5\vec{a} - 2\vec{b} $$

6. a) Column vector P. Step 1: Substitute the given vectors $\vec{a}$ and $\vec{b}$ into the expression for $\vec{p}$ . $\vec{p} = 5\vec{a} - 2\vec{b}$ $\vec{p} = 5 \begin{pmatrix} 3 \\ 2 \end{pmatrix} - 2 \begin{pmatrix} 4 \\ 2 \end{pmatrix}$ Step 2: Perform scalar multiplication.

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Asked on April 24, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 24, 2026

6. a) Column vector P. Step 1: Substitute the given vectors a and b into the expression for p. p = 5a - 2b p = 5 3 \\ 2 - 2 4 \\ 2 Step 2: Perform scalar multiplication. p = 5 × 3 \\ 5 × 2 - 2 × 4 \\