Exercises
Determinants
Cofactors
Cramer's Rule
Partitioned Matrices
Elementary Matrices
Inverse Matrices
Elimination:
A =
LU
-
Without row exchange, use elementary matrices to find LU-factorizations for
the following matrices.
\[
\mbox{(a)} \quad \begin{bmatrix} -8&-5&-6&5 \\ 3&-6&7&-3 \\ -10&-3&4&2 \\
5&-5&7&8 \end{bmatrix} ; \qquad \mbox{(b)} \quad \begin{bmatrix} 2&1&-1&0 \\
4&3&3&1 \\ 8&7&9&5 \\ 6&7&9&8 \end{bmatrix} ; \qquad \mbox{(c)} \quad
\]
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PLU Factorization
-
Using row exchange and elementary matrices, find PLU-factorizations for
the following matrices.
-
\[
\mbox{(a)} \quad \begin{bmatrix} -9&8&-3&0 \\ -9&-5&5&1 \\ 6&7&3&5 \\ 6&-2&6&7
\end{bmatrix} , \qquad \mbox{(b)} \quad \begin{bmatrix} 5&2&-5&0 \\
6&-8&-8&-4 \\ 2&9&-9&2 \\ -1&6&6&-6 \end{bmatrix}
\]
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Reflection
Givens Rotation
Special Matrices
