Question

MATRIX QUESTION

Answer 1

Matrix A,B, and C are defined by:

\[A = \left[\begin{matrix}5 & 1 \\ 7 & 2\end{matrix}\right], B= \left[\begin{matrix}2 & 4 \\ -3 & 15\end{matrix}\right], C=\left[\begin{matrix}9 & -7 \\ 8 & 2\end{matrix}\right]\]

Let X be an unknown 2x2 matrix satisfying the equation AX+B=C. This equation may by rewriting it in the form \[X=A ^{-1}D\], where D is a 2x2 matrix.

(a) Write down \[A ^{-1}\]Matrix A,B, and C are defined by:

\[A = \left[\begin{matrix}5 & 1 \\ 7 & 2\end{matrix}\right], B= \left[\begin{matrix}2 & 4 \\ -3 & 15\end{matrix}\right], C=\left[\begin{matrix}9 & -7 \\ 8 & 2\end{matrix}\right]\]

Let X be an unknown 2x2 matrix satisfying the equation AX+B=C. This equation may by rewriting it in the form \[X=A ^{-1}D\], where D is a 2x2 matrix.

(a) Write down \[A ^{-1}\]

(b) Find D

(c) Find X.

Answer 2

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