Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} 1 \ -1 end{pmatrix}$. Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula $\(end{pmatrix}). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \text{proj}_\mathbf{a} \mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{| \mathbf{a} |^2} \mathbf{a}$.

Question

Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} 1 \ -1 end{pmatrix}$. Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula $\(end{pmatrix}). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \text{proj}_\mathbf{a} \mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{| \mathbf{a} |^2} \mathbf{a}$.

Accepted Answer

$\begin{pmatrix} \frac{5}{13} \frac{15}{13} \end{pmatrix} $

Post Utme Esut 2025 Mathematics Question 26

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