# simplify the following matrix expression: begin{bmatrix}1 & 5 2 & -3-3&7 end{bmatrix}-2begin{bmatrix}2 & -3 8 & 5-1&-1 end{bmatrix}=?

simplify the following matrix expression:
$\left[\begin{array}{cc}1& 5\\ 2& -3\\ -3& 7\end{array}\right]-2\left[\begin{array}{cc}2& -3\\ 8& 5\\ -1& -1\end{array}\right]=?$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Aniqa O'Neill
Step 1
Given that:
$|\begin{array}{cc}1& 5\\ 2& -3\\ -3& 7\end{array}|-2|\begin{array}{cc}2& -3\\ 8& 5\\ -1& -1\end{array}|$
To find:
We have to simplify the given expression.
First we find:
$2|\begin{array}{cc}2& -3\\ 8& 5\\ -1& -1\end{array}|$
In this multiplication each entry in the matrix is multiplied by the scalar 2.
$⇒2|\begin{array}{cc}2& -3\\ 8& 5\\ -1& -1\end{array}|=|\begin{array}{cc}2\left(2\right)& 2\left(-3\right)\\ 2\left(8\right)& 2\left(5\right)\\ 2\left(-1\right)& 2\left(-1\right)\end{array}|$
$2|\begin{array}{cc}2& -3\\ 8& 5\\ -1& -1\end{array}|=|\begin{array}{cc}4& -6\\ 16& 10\\ -2& -2\end{array}|$
Step 2
$⇒|\begin{array}{cc}1& 5\\ 2& -3\\ -3& 7\end{array}|-2|\begin{array}{cc}2& -3\\ 8& 5\\ -1& -1\end{array}|=|\begin{array}{cc}1& 5\\ 2& -3\\ -3& 7\end{array}|-|\begin{array}{cc}4& -6\\ 16& 10\\ -2& -2\end{array}|$
Now we substracting this two matrices.
Here the order of matrices is same.
So, the difference between this two matrices is obtained by substracting the corresponding elements of the matrices.
We get,
$|\begin{array}{cc}1& 5\\ 2& -3\\ -3& 7\end{array}|-2|\begin{array}{cc}2& -3\\ 8& 5\\ -1& -1\end{array}|=|\begin{array}{cc}1-4& 5-\left(-6\right)\\ 2-16& -3-10\\ -3-\left(-2\right)& 7-\left(-2\right)\end{array}|$
$=|\begin{array}{cc}-3& 5+6\\ -14& -13\\ -3+2& 7+2\end{array}|$
$⇒|\begin{array}{cc}1& 5\\ 2& -3\\ -3& 7\end{array}|-2|\begin{array}{cc}2& -3\\ 8& 5\\ -1& -1\end{array}|=|\begin{array}{cc}-3& 11\\ -14& -13\\ -1& 9\end{array}|$
Hence the solution.
Jeffrey Jordon