Question

Consider two linearly independent vectors ${\overrightarrow{\mathbf{v}}}_{\mathbf{1}}\mathbf{=}\left[\begin{array}{c}a\\ b\end{array}\right]$ and${\overrightarrow{\mathbf{v}}}_{\mathbf{2}}\mathbf{=}\left[\begin{array}{c}c\\ d\end{array}\right]$ in ${\mathbf{R}}^{\mathbf{2}}$. Draw sketches to illustrate the Gram-Schmidt process for role="math" localid="1660117977205" ${\overrightarrow{\mathbf{v}}}_{\mathbf{1}}$and ${\overrightarrow{\mathbf{v}}}_{\mathbf{2}}$.

Short answer

The solution is the vectors are shown graphically.

Step-by-step solution

`Explanation of the solution

Consider the two vectors as follows:

${\overrightarrow{\mathrm{v}}}_1=\left[\begin{array}{c}\mathrm{a}\\ \mathrm{b}\end{array}\right]$and ${\overrightarrow{\mathrm{v}}}_2=\left[\begin{array}{c}\mathrm{c}\\ \mathrm{d}\end{array}\right]$.

It will perform the Gram Schmidt process for${\overrightarrow{\mathrm{v}}}_1$and${\overrightarrow{\mathrm{v}}}_2$graphically on the given vectors.

The vectors are shown graphically as follows:

Thus, the vectors are shown graphically.