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marusya05 [52]
3 years ago
14

Suppose that det(a) = a b c d e f g h i = 2 and find the determinant of the given matrix. a b c −4d −4e −4f a + g b + h c + i

Mathematics
1 answer:
zhuklara [117]3 years ago
5 0
I'll go out on a limb and suppose you're given the matrix

\mathbf A=\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}

and you're asked to find the determinant of \mathbf B, where

\mathbf B=\begin{bmatrix}a&b&c\\-4d&-4e&-4f\\a+g&b+h&c+i\end{bmatrix}

and given that \det\mathbf A=2.

There are two properties of the determinant that come into play here:

(1) Whenever a single row/column is scaled by a constant k, then the determinant of the matrix is scaled by that same constant;

(2) Adding/subtracting rows does not change the value of the determinant.

Taken together, we have that

\det\mathbf B=-4\det\mathbf A=-8
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