Question

Find $A B$ and $B A$ in each case. $$\text { LetA }=\left[\begin{array}{r}2 \\-3 \\1\end{array}\right], B=\left[\begin{array}{lll} 2 & 3 & 4\end{array}\right], C=\left[\begin{array}{ll}2 & 3 \\4 & 5 \\1 & 0\end{array}\right]$$ $$D=\left[\begin{array}{rrr}2 & -1 & 1 \\0 & 3 & 2\end{array}\right], \text { and } E=\left[\begin{array}{lll}1 & 1 & 1 \\0 & 1 & 1 \\0 & 0 & 1\end{array}\right]$$ Find the following if possible. $$D C$$

          Find $A B$ and $B A$ in each case.
$$\text { LetA }=\left[\begin{array}{r}2 \\-3 \\1\end{array}\right], B=\left[\begin{array}{lll}
2 & 3 & 4\end{array}\right], C=\left[\begin{array}{ll}2 & 3 \\4 & 5 \\1 & 0\end{array}\right]$$
$$D=\left[\begin{array}{rrr}2 & -1 & 1 \\0 & 3 & 2\end{array}\right], \text { and } E=\left[\begin{array}{lll}1 & 1 & 1 \\0 & 1 & 1 \\0 & 0 & 1\end{array}\right]$$
Find the following if possible.
$$D C$$

Added by Sean A.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Avi Zellman

Step 1

For matrix $A$ and vector $B$, we have: $$AB = \left[\begin{array}{r}2 \\-3 \\1\end{array}\right]\left[\begin{array}{lll}2 & 3 & 4\end{array}\right] = \left[\begin{array}{lll}4 & 6 & 8 \\-6 & -9 & -12 \\2 & 3 & 4\end{array}\right]$$ $$BA = Show more…

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Find $A B$ and $B A$ in each case. $$\text { LetA }=\left[\begin{array}{r}2 \\-3 \\1\end{array}\right], B=\left[\begin{array}{lll} 2 & 3 & 4\end{array}\right], C=\left[\begin{array}{ll}2 & 3 \\4 & 5 \\1 & 0\end{array}\right]$$ $$D=\left[\begin{array}{rrr}2 & -1 & 1 \\0 & 3 & 2\end{array}\right], \text { and } E=\left[\begin{array}{lll}1 & 1 & 1 \\0 & 1 & 1 \\0 & 0 & 1\end{array}\right]$$ Find the following if possible. $$D C$$