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.
[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.
