91影视

For each matrix in exercises 1 through 13, find vectors that span the kernel of . Use paper and pencil.

For each matrix $\mathbf{A}$in exercises 14 through 16, find vectors that span the image of $\mathbf{A}$. Give as few vectors as possible. Use paper and pencil.

$\mathit{A}\mathbf{=}\left[\begin{array}{ccc}1& 2& 3\\ 1& 2& 3\\ 1& 2& 3\end{array}\right]$

For each matrix $\mathit{A}$in Exercise 14 through 16, find vectors that span the image of $\mathit{A}$. Give as few vectors as possible. Use paper and pencil.

$\mathit{A}\mathbf{=}\mathbf{\left[}\begin{array}{cccc}\mathbf{1}& \mathbf{1}& \mathbf{1}& \mathbf{1}\\ \mathbf{1}& \mathbf{2}& \mathbf{3}& \mathbf{4}\end{array}\mathbf{\right]}$

For each matrix$\mathit{A}$ in Exercise 14 through 16, find vectors that span the image of $\mathit{A}$. Give as few vectors as possible. Use paper and pencil.

$\mathit{A}\mathbf{=}\mathbf{\left[}\begin{array}{cc}\mathbf{1}& \mathbf{1}\\ \mathbf{1}& \mathbf{2}\\ \mathbf{1}& \mathbf{3}\\ \mathbf{1}& \mathbf{4}\end{array}\mathbf{\right]}$

For each matrix $\mathit{A}$in Exercise 17 through 22, describe the image of the transformation $\mathit{T}\left(\stackrel{鈫�}{x}\right)\mathbf{=}\mathit{A}\stackrel{\mathbf{鈫�}}{\mathbf{x}}$geometrically (as a line, plane, etc. in ${\mathbf{鈩�}}^{\mathbf{2}}\mathbf{}\mathbf{\text{and}}\mathbf{}{\mathbf{鈩�}}^{\mathbf{3}}$.

$\mathit{A}\mathbf{=}\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$

For each matrix in Exercise 17 through 22, describe the image of the transformation $\mathit{T}\left(\stackrel{鈫�}{x}\right)\mathbf{=}\mathit{A}\stackrel{\mathbf{鈫�}}{\mathbf{x}}$geometrically (as a line, plane, etc. in ${\mathbf{鈩�}}^{\mathbf{2}}\mathbf{}\mathbf{\text{and}}\mathbf{}{\mathbf{鈩�}}^{\mathbf{3}}$.

$\mathit{A}\mathbf{=}\left[\begin{array}{cc}1& 4\\ 3& 12\end{array}\right]$

For each matrix in Exercise 17 through 22, describe the image of the transformation $\mathit{T}\left(\stackrel{鈫�}{x}\right)\mathbf{=}\mathit{A}\stackrel{\mathbf{鈫�}}{\mathbf{x}}$geometrically (as a line, plane, etc. in ${\mathbf{鈩�}}^{\mathbf{2}}\mathbf{}\mathbf{\text{and}}\mathbf{}{\mathbf{鈩�}}^{\mathbf{3}}$.

$\mathit{A}\mathbf{=}\mathbf{\left[}\begin{array}{cccc}\mathbf{1}& \mathbf{2}& \mathbf{3}& \mathbf{4}\\ \mathbf{-}\mathbf{2}& \mathbf{-}\mathbf{4}& \mathbf{-}\mathbf{6}& \mathbf{-}\mathbf{8}\end{array}\mathbf{\right]}$

For each matrix in Exercise 17 through 22, describe the image of the transformation $\mathit{T}\mathbf{\left(}\stackrel{\mathbf{鈫�}}{\mathbf{x}}\mathbf{\right)}\mathbf{=}\mathit{A}\stackrel{\mathbf{鈫�}}{\mathbf{x}}$geometrically (as a line, plane, etc. in ${\mathbf{鈩�}}^{\mathbf{2}}\mathbf{}\mathbf{\text{and}}\mathbf{}{\mathbf{鈩�}}^{\mathbf{3}}$.

role="math" localid="1664181795984" $\mathit{A}\mathbf{=}\mathbf{\left[}\begin{array}{ccc}\mathbf{2}& \mathbf{1}& \mathbf{3}\\ \mathbf{3}& \mathbf{4}& \mathbf{2}\\ \mathbf{6}& \mathbf{5}& \mathbf{7}\end{array}\mathbf{\right]}$

For each matrix A in Exercise 17 through 22, describe the image of the transformation $\mathbf{T}\left(\stackrel{鈫�}{x}\right)\mathbf{=}\mathbf{A}\stackrel{\mathbf{鈫�}}{\mathbf{x}}$geometrically (as a line, plane, etc. in ${\mathbf{鈩�}}^{\mathbf{2}}\mathbf{}\mathbf{\text{and}}\mathbf{}{\mathbf{鈩�}}^{\mathbf{3}}$.

$\mathit{A}\mathbf{=}\left[\begin{array}{ccc}4& 7& 3\\ 1& 9& 2\\ 5& 6& 8\end{array}\right]$

For each matrix A in Exercise 17 through 22, describe the image of the transformation $\mathbf{T}\mathbf{\left(}\stackrel{\mathbf{鈫�}}{\mathbf{x}}\mathbf{\right)}\mathbf{=}\mathbf{A}\stackrel{\mathbf{鈫�}}{\mathbf{x}}$geometrically (as a line, plane, etc. in ${\mathbf{鈩�}}^{\mathbf{2}}\mathbf{}\mathbf{\text{and}}\mathbf{}{\mathbf{鈩�}}^{\mathbf{3}}$.

$\mathit{A}\mathbf{=}\mathbf{\left[}\begin{array}{ccc}\mathbf{1}& \mathbf{1}& \mathbf{1}\\ \mathbf{1}& \mathbf{1}& \mathbf{1}\\ \mathbf{1}& \mathbf{1}& \mathbf{1}\end{array}\mathbf{\right]}$