Q. 7 - Precalculus Enhanced with Graphing Utilities

Question

True or False 

The identity matrix has properties similar to

those of the real number 1.

Step-by-Step Solution

Answer

False.

Step 1. Given Information

An identity matrix.

Step 2. Calculation

$$\begin{gathered} consider, \\ A=\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right] \\ A{I}_2=\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right]\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right] \\ =\left[\begin{array}{cc}1\times 1+3\times 0& 1\times 0+3\times 1\\ 2\times 1+4\times 0& 2\times 0+4\times 1\end{array}\right] \\ =\left[\begin{array}{cc}2& 3\\ 2& 5\end{array}\right] \sin ce each entity is not increased by one therefore its false. \end{gathered}$$