(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [tex]det\left[

\begin {array}{ccc}

a&1&d\\

\noalign{\medskip}

b&1&e\\

\noalign{\medskip}

c&1&f

\end {array}

\right]=-4

[/tex] and [tex]det\left[

\begin {array}{ccc}

a&1&d\\

\noalign{\medskip}

b&2&e\\

\noalign{\medskip}

c&3&f

\end {array}

\right]=-1

[/tex],

then [tex]det\left[

\begin {array}{ccc}

a&8&d\\

\noalign{\medskip}

b&8&e\\

\noalign{\medskip}

c&8&f

\end {array}

\right]=___

[/tex]

and [tex]det\left[

\begin {array}{ccc}

a&-1&d\\

\noalign{\medskip}

b&-4&e\\

\noalign{\medskip}

c&-7&f

\end {array}

\right]=___

[/tex]

3. The attempt at a solution

For the first question, I'm pretty sure that I can factor out an 8 as it is a scalar multiple of the second column. One of the properties of determinants is that if a row or column is multiplied by a scalar, then we can factor the scalar out and then multiply the determinant by that scalar. Thus, the answer would be -32.

However, I am really stumped by the second question. I am sure that the scalar -1 is somehow multiplied into the matrix, but I am not sure how the numbers were obtained. I'm thinking that each row must have resulted from the scalar multiple of another row. However, if that's the case, then why are the unknowns unaffected?

I am seriously at my wit's end and any direction would be helpful.

Thank you!

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# Homework Help: Linear Algebra - Determinants

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