College

Solve for [tex]X[/tex]:

[tex]
\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}
X =
\begin{bmatrix}
-8 & -6 \\
-9 & 9
\end{bmatrix}
[/tex]

[tex]
X =
\begin{bmatrix}
-8 & -6 \\
-9 & 9
\end{bmatrix}
[/tex]

Answer :

To solve this problem, we're working with two matrices. We need to find matrix [tex]\( X \)[/tex] in the equation:

[tex]\[
\left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right] X = \left[\begin{array}{cc}-8 & -6 \\ -9 & 9\end{array}\right]
\][/tex]

This is a matrix equation where the first matrix on the left is the identity matrix. The identity matrix, denoted as [tex]\( I \)[/tex], has the property that when you multiply any matrix [tex]\( A \)[/tex] by [tex]\( I \)[/tex], the result is the matrix [tex]\( A \)[/tex] itself. Mathematically, this is expressed as [tex]\( I \cdot A = A \)[/tex].

In this case, the identity matrix is:

[tex]\[
I = \left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right]
\][/tex]

According to the property of the identity matrix, multiplying it by matrix [tex]\( X \)[/tex] gives us:

[tex]\[
I \cdot X = X
\][/tex]

In our problem, we have:

[tex]\[
I \cdot X = \left[\begin{array}{cc}-8 & -6 \\ -9 & 9\end{array}\right]
\][/tex]

So [tex]\( X \)[/tex] must be exactly:

[tex]\[
X = \left[\begin{array}{cc}-8 & -6 \\ -9 & 9\end{array}\right]
\][/tex]

This means the matrix [tex]\( X \)[/tex] is:

[tex]\[
\left[\begin{array}{cc}-8 & -6 \\ -9 & 9\end{array}\right]
\][/tex]

Thus, the solution to the equation is matrix [tex]\( X \)[/tex] as shown above.