Question

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Solve the matrix equation.
X+ 2 -5 8 6 -1 9
-8 3 0 = -5 2 8

Answer 1

Is that \(x\) a matrix? And the equation...?\[X+\begin{pmatrix}2&-5&8\\-8&3&0\end{pmatrix}=\begin{pmatrix}6&-1&9\\-5&2&8\end{pmatrix}\]

Answer 2

If that's right, then matrix addition can only be done if \(X\) has the same dimensions as the other two matrices.

Let
\[X=\begin{pmatrix}a&b&c\\d&e&f\end{pmatrix}\]
So you have the equation
\[\begin{pmatrix}a&b&c\\d&e&f\end{pmatrix}+\begin{pmatrix}2&-5&8\\-8&3&0\end{pmatrix}=\begin{pmatrix}6&-1&9\\-5&2&8\end{pmatrix}\]
Adding, you get
\[\begin{pmatrix}a+2&b-5&c+8\\d-8&e+3&f+0\end{pmatrix}=\begin{pmatrix}6&-1&9\\-5&2&8\end{pmatrix}\]
Now each element in the matrices must match up:
\[\begin{cases}a+2=6\\b-5=-1\\c+8=9\\d-8=-5\\e+3=2\\f+0=8\end{cases}\]
Solve for \(a,b,c,d,e,f\).

Answer 3

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