If $$ M=\left[\begin{array}{lll}a & b & c \ d & e & f \ g & h & i\end{array} ight] $$ and $$ \operatorname{det}(M)=6 $$ $$ \operatorname{Det}\left(\left[\begin{array}{ccc}4 a & 4 b & 4 c \ d & e & f \ g & h & i\end{array} ight] ight)= $$ Submit Question

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If $$ M=\left[\begin{array}{lll}a & b & c \ d & e & f \ g & h & i\end{array}ight] $$ and $$ \operatorname{det}(M)=6 $$ $$ \operatorname{Det}\left(\left[\begin{array}{ccc}4 a & 4 b & 4 c \ d & e & f \ g & h & i\end{array}ight]ight)= $$ Submit Question

UpStudy AI · Accepted Answer

Since only the first row is multiplied by 4, we can factor out the 4 from the first row. This gives:

$$
\operatorname{det}\left(\begin{bmatrix} 4a & 4b & 4c \ d & e & f \ g & h & i \end{bmatrix}\right) = 4 \times \operatorname{det}(M)
$$

Given $$\operatorname{det}(M) = 6$$, we have:

$$
4 \times 6 = 24
$$
The determinant is 24.

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