Each of the given linear systems is in row echelon form. Solve the system. (a) x + y - z + 2w = 4 w = 5 (b) .{ - y + z = 0 y +2z=0 z =1

Section 1.5 — Matrices Saturday, September 2, 2017 7:40 PM Definition 1: A m x n matrix A is denoted: Example 1: Determine and for the following matrix: Definition 2: Let and be m x n matrices.The m x n matrix A + B is defined by: **NOTE: Matrices musthave the samenumber of rows and variables in order to add them. Example 2: Find A + B for: Definition 3: If is an m x n matrix and if is a scalar,then the m x n matrix is given by: In other words, is the matrix obtained by multiplying eachcomponentof A by . If for i , , , m and j , , , n Example 3: Definition 4: Two matrices are equal if: 1. They have the samesize. 2. Correspondingcomponentsare equal. Example 4: Are the following matricesequal Example 4: Are the following matricesequal Yes, these matricesare equal. Definition 5: An m x n matrix with all componentsequal to zero is calledthe m x n zero matrix. Example 5: Is the following matrix a zero matrix Yes, the following is an example of a 2 x 4 zero matrix. Theorem 1: Let , , , , 1. A+0 = A, where 0 is the m x n zero matrix. 2. A+B=B+A 3. (A+B)+C = A+(B+C) 4. 5. 6. Proof 1.1: , Proof 1.2: , (Since real