Help with linear algebra HW. Please show work!

Given that

$$\begin{vmatrix} a & b & c \\ 10d & 10e & 10e \\ g & h & i \end{vmatrix}=7,$$ find the value of
$$\begin{vmatrix} d & e & f \\ a-2g & b-2h & c-2i \\ 5g & 5h & 5i \end{vmatrix}. $$

Hint: Use row operations to transform first to

$$\begin{pmatrix} a & b & c \\ d & e & f \\ g & h& i \end{pmatrix}, $$ then continue to get the ending matrix, keeping track of how your operations change the determinant

  • It's hard to read the formulas in your question. Why don't you post a picture of the question?

  • Didn’t realize I could do that. I just uploaded a picture.

    • I revised your question. The main change was that I used "pmatrix" in the LaTeX code.

    • And also vmatrix!


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