## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 8 - Section 8.1 - Matrix Solutions to Linear Systems - Exercise Set - Page 895: 51

#### Answer

Collection of elements.

#### Work Step by Step

A matrix is defined as the collection of numbers or elements that can be arranged in rows and columns in the form of an array. There are different kinds of matrices. Column matrix: a matrix having a single column. Row matrix: a matrix having a single row. Square matrix: a matrix having number of rows are equal to number of columns. Diagonal matrix: a diagonal matrix that has diagonal elements equal. Scalar matrix: a square matrix in which all non-diagonal elements are zero. Identity matrix: a square matrix in which diagonal elements are all 1 and the left over elements are zero. Example: Column matrix is given by: $\left[ \begin{matrix} 1 \\ 5 \\ 9 \\ \end{matrix} \right]$ Row matrix is given by: $\left[ \begin{matrix} 4 & 1 & 9 \\ \end{matrix} \right]$ Square matrix is given by: $\left[ \begin{matrix} 1 & 3 \\ 6 & 9 \\ \end{matrix} \right]$ Diagonal matrix is given by: $\left[ \begin{matrix} 4 & 0 & 0 \\ 0 & 8 & 0 \\ 0 & 0 & 6 \\ \end{matrix} \right]$ Scalar matrix is given by: $\left[ \begin{matrix} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \\ \end{matrix} \right]$ Identity matrix is given by: $\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]$

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