For matrices A through H as given, use a calculator to...

For matrices $A$ through $H$ as given, use a calculator to perform the indicated operation(s), if possible. If an operation cannot be completed, state why. $$\begin{aligned}&A=\left[\begin{array}{rr}-5 & 4 \\3 & 9\end{array}\right] \quad =\left[\begin{array}{ll}1 & 0 \\0 & 1\end{array}\right]\\&C=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{3} \\\sqrt{3} & 2 \sqrt{3}\end{array}\right] \quad D=\left[\begin{array}{lll}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array}\right]\\&E=\left[\begin{array}{ccc}1 & -2 & 0 \\0 & -1 & 2 \\ 4 & 3 & -6\end{array}\right] F=\left[\begin{array}{ccc}-0.52 & 0.002 & 1.032 \\1.021 & -1.27 & 0.019\end{array}\right]\\&G=\left[\begin{array}{ccc}0 & \frac{3}{4} & \frac{1}{4} \\\frac{-1}{2} & \frac{3}{8} & \frac{1}{8} \\\frac{-1}{4} & \frac{11}{16} & \frac{1}{16}\end{array}\right] \quad H=\left[\begin{array}{cc}\frac{-3}{19} & \frac{4}{57} \\\frac{1}{19} & \frac{5}{57}\end{array}\right] \end{aligned}$$ $$A-H$$

For matrices $A$ through $H$ as given, use a calculator to perform the indicated operation(s), if possible. If an operation cannot be completed, state why.
$$\begin{aligned}&A=\left[\begin{array}{rr}-5 & 4 \\3 & 9\end{array}\right] \quad =\left[\begin{array}{ll}1 & 0 \\0 & 1\end{array}\right]\\&C=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{3} \\\sqrt{3} & 2 \sqrt{3}\end{array}\right] \quad D=\left[\begin{array}{lll}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array}\right]\\&E=\left[\begin{array}{ccc}1 & -2 & 0 \\0 & -1 & 2 \\
4 & 3 & -6\end{array}\right] F=\left[\begin{array}{ccc}-0.52 & 0.002 & 1.032 \\1.021 & -1.27 & 0.019\end{array}\right]\\&G=\left[\begin{array}{ccc}0 & \frac{3}{4} & \frac{1}{4} \\\frac{-1}{2} & \frac{3}{8} & \frac{1}{8} \\\frac{-1}{4} & \frac{11}{16} & \frac{1}{16}\end{array}\right] \quad H=\left[\begin{array}{cc}\frac{-3}{19} & \frac{4}{57} \\\frac{1}{19} & \frac{5}{57}\end{array}\right]
\end{aligned}$$
$$A-H$$

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Key Concepts

Dimension Compatibility

For subtraction (or addition) of matrices to be defined, the matrices must have identical dimensions. This compatibility ensures that each element in one matrix aligns with an element in the other, making it possible to perform element-by-element operations.

Matrix Subtraction

Matrix subtraction is the process of subtracting corresponding elements of two matrices that share the same dimensions. It is an element-wise operation, meaning that every element in the first matrix is subtracted by the corresponding element in the second matrix, resulting in a new matrix of the same size.

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