The course contains concepts and techniques of linear algebra. The course topics include systems of linear equations, determinants, vectors and vector spaces, eigenvalues and eigenvectors and singular value decomposition of matrix.

\(\begin{bmatrix}5 & -7 & 2 & 2\\ 0 & 3 & 0 & -4\\ -5 & -8 & 0 & 3\\ 0 & 5 & 0 & -6\end{bmatrix}\)

A = \(\begin{bmatrix}-1 & -3 & 2\\ -5 & -9 & 1\end{bmatrix}\), and v = \(\begin{bmatrix}5\\ -3\\ -2\end{bmatrix}\)

\(\begin{bmatrix}3 & 6 & -4\\ 0 & 0 & -6\\ 0 & 0 & -2 \end{bmatrix}\)

T(e_{1}) = \(\begin{bmatrix}5\\ 1\\ -2\end{bmatrix}\) and T(e_{2}) = \(\begin{bmatrix}0\\ -1\\ 8\end{bmatrix}\)

find a formula for the image of an arbitrary x in R^{2}. That is, find T(x) for x in R^{2}.

a = \(\begin{bmatrix}1\\ -3\\ 2\end{bmatrix}\), b = \(\begin{bmatrix}0\\ -1\\ 3\end{bmatrix}\)

A = \(\begin{bmatrix}-2 & 8 & -1\\ 0 & 0 & 0\\ 0 & -5 & 3\end{bmatrix}\)

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