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Further matrices — Question 272

Original QCE Vault practice · 5 marks

Q272 · Practice questionTechnology-activeSimple familiar5 marks

QUESTION 272 (5 marks)

Let
A=(110011101),B=(100010001),C=(225732210).A=\begin{pmatrix}1&1&0\\0&1&1\\1&0&1\end{pmatrix},\quad B=\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix},\quad C=\begin{pmatrix}2&2&5\\7&3&2\\2&1&0\end{pmatrix}.
A 3×33\times3 matrix X satisfies XA+XB=CXA+XB=C.
a)
Rearrange the equation to isolate X. State the side on which the inverse must be multiplied.
[2 marks]
b)
Use matrix technology to determine X and verify by multiplication.
[3 marks]
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