Question

Refer to the matrices $$A=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right] \text { and } B=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]$$ If $B A=0,$ how are $a, b, c,$ and $d$ related? Use this relationship to provide several examples of $2 \times 2$ matrices $A$ with no zero entries that satisfy $B A=0$

          Refer to the matrices
$$A=\left[\begin{array}{ll}
a & b \\
c & d
\end{array}\right] \text { and } B=\left[\begin{array}{ll}
1 & 1 \\
1 & 1
\end{array}\right]$$
If $B A=0,$ how are $a, b, c,$ and $d$ related? Use this relationship to provide several examples of $2 \times 2$ matrices $A$ with no zero entries that satisfy $B A=0$

Added by John S.

Elementary and Intermediate Algebra

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

Instant Answer

Solved by Expert Nicole Hoffman

Step 1

First, we need to find the product $BA$: $$BA=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]=\left[\begin{array}{ll} a+c & b+d \\ a+c & b+d \end{array}\right]$$ For $BA$ to be zero, we must have Show more…

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Refer to the matrices $$A=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right] \text { and } B=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]$$ If $B A=0,$ how are $a, b, c,$ and $d$ related? Use this relationship to provide several examples of $2 \times 2$ matrices $A$ with no zero entries that satisfy $B A=0$