IB Mathematics Applications & Interpretation Question Type 1: Performing Simple Linear Operations on Matrices Exercises

Simplify $3A+2B-A$ for $$A=\left(\begin{array}{cc}2& 1\\ 0& 3\end{array}\right),B=\left(\begin{array}{cc}-1& 4\\ 5& 2\end{array}\right).$$

Compute $$3E-F$$ for $$E=\left(\begin{array}{ccc}1& -1& 2\\ 0& 3& -2\\ 4& 1& 0\end{array}\right),F=\left(\begin{array}{ccc}2& 0& -1\\ 3& -1& 1\\ 0& 2& 4\end{array}\right).$$

If $X+2A=3B$ and $$A=\left(\begin{array}{cc}1& 0\\ -1& 2\end{array}\right),B=\left(\begin{array}{cc}2& 3\\ 1& 0\end{array}\right),$$ find $X$.

Evaluate $$5\left(\begin{array}{cc}0& -3\\ 2& 1\end{array}\right)-3\left(\begin{array}{cc}1& 2\\ 0& 4\end{array}\right).$$

Calculate $$4\left(\begin{array}{cc}2& 1\\ 3& 5\end{array}\right)+2\left(\begin{array}{cc}1& 0\\ -1& 2\end{array}\right).$$

Given $$A=\left(\begin{array}{cc}1& -2\\ 3& 4\end{array}\right),B=\left(\begin{array}{cc}2& 0\\ -1& 5\end{array}\right),$$ find $2A+3B$.

Verify the distributive property $k(A+B)=kA+kB$ by computing both sides for $$k=2,A=\left(\begin{array}{cc}1& 2\\ 3& -1\end{array}\right),B=\left(\begin{array}{cc}0& 4\\ -2& 5\end{array}\right).$$

Compute $3A$ where $$A=\left(\begin{array}{cc}2& -1\\ 4& 0\end{array}\right).$$

Let $$C=\left(\begin{array}{ccc}-1& 2& 0\\ 3& 1& -2\end{array}\right),D=\left(\begin{array}{ccc}2& -3& 4\\ 0& 5& -1\end{array}\right).$$

Compute $C-2D$.

Calculate $-3C+4D$.

Simplify $$2(A+B)-(A-B)$$ where $$A=\left(\begin{array}{cc}1& 2\\ 3& 0\end{array}\right),B=\left(\begin{array}{cc}0& -1\\ 4& 5\end{array}\right).$$

Compute $-2B$ where $$B=\left(\begin{array}{cc}1& 3\\ -2& 4\end{array}\right).$$