Processing math: 50%
Back to the class
Problems #4 on pg.121 and #1, pg.167 are graded.
#4,pg.121: Compute the product of partitioned matrices [I0−EI][WXYZ] (assume the partitions chosen make sense for multiplication).
Solution: Compute the same way as "normal" matrix multiplication:
[I0−EI][WXYZ]=[IW+0YIX+0Z−EW+IY−EX+IZ]=[WX−EW+Y−EX+Z].
#1, pg.167: Compute det.
Solution: Compute
\begin{array}{ll}
\det \begin{bmatrix} 3&0&4 \\ 2&3&2 \\ 0&5&-1 \end{bmatrix} &= 3 \det \begin{bmatrix} 3 & 2 \\ 5 & -1 \end{bmatrix} - 0 \det \begin{bmatrix} 2&2 \\ 0&-1 \end{bmatrix} + 4 \det \begin{bmatrix} 2 & 3 \\ 0 & 5 \end{bmatrix} \\
&= 3(-3-10)-0(-2-0)+4(10-0) \\
&= -39-0+40 \\
&= 1.
\end{array}
