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Step 2 Use row operations to find an equivalent matrix in the row-echelon form. Recall that a matrix in the row- echelon form has a stair-step pattern with 1 as the first nonzero entry. 1 2 3 0 1 2 Example: Write the row operation you will perform to make the first entry in the second row equal to 0. Add -1 v -1 times Row 1 to Row 2. Perform the operation and write the equivalent matrix. 2 |12 12 -1 R1 + R2 → |-3 -3 |-12 -12 Step 3 Write the row operation you will use to make the first nonzero entry in each row equal to 1. Multiply Row 1 by 1/2 and Row 2 by |× . Perform the operation and write the equivalent matrix. 1/2 R1+ X R2 →

Step 2 Use row operations to find an equivalent matrix in the row-echelon form. Recall that a matrix in the row- echelon form has a stair-step pattern with 1 as the first nonzero entry. 1 2 3 0 1 2 Example: Write the row operation you will perform to make the first entry in the second row equal to 0. Add -1 v -1 times Row 1 to Row 2. Perform the operation and write the equivalent matrix. 2 |12 12 -1 R1 + R2 → |-3 -3 |-12 -12 Step 3 Write the row operation you will use to make the first nonzero entry in each row equal to 1. Multiply Row 1 by 1/2 and Row 2 by |× . Perform the operation and write the equivalent matrix. 1/2 R1+ X R2 →

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 32E
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Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution. S2x + 6y = 12 2x + 3y = o Step 1 Write the associated augmented matrix for the given linear system. Recall that since there are two equations in the system, the matrix will have two rows. Use the coefficients of x and y as entries of the first column and second column, respectively. Use the constant terms in the last column. 2 6: 12 12 2 3: 0 V
Transcribed Image Text:Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution. S2x + 6y = 12 2x + 3y = o Step 1 Write the associated augmented matrix for the given linear system. Recall that since there are two equations in the system, the matrix will have two rows. Use the coefficients of x and y as entries of the first column and second column, respectively. Use the constant terms in the last column. 2 6: 12 12 2 3: 0 V
Step 2 Use row operations to find an equivalent matrix in the row-echelon form. Recall that a matrix in the row- echelon form has a stair-step pattern with 1 as the first nonzero entry. 1 2 3 0 1 2 Example: Write the row operation you will perform to make the first entry in the second row equal to 0. Add -1 v -1 times Row 1 to Row 2. Perform the operation and write the equivalent matrix. 2 |12 12 -1 R1 + R2 → |-3 -3 |-12 -12 Step 3 Write the row operation you will use to make the first nonzero entry in each row equal to 1. Multiply Row 1 by 1/2 and Row 2 by |× . Perform the operation and write the equivalent matrix. 1/2 R1+ X R2 →
Transcribed Image Text:Step 2 Use row operations to find an equivalent matrix in the row-echelon form. Recall that a matrix in the row- echelon form has a stair-step pattern with 1 as the first nonzero entry. 1 2 3 0 1 2 Example: Write the row operation you will perform to make the first entry in the second row equal to 0. Add -1 v -1 times Row 1 to Row 2. Perform the operation and write the equivalent matrix. 2 |12 12 -1 R1 + R2 → |-3 -3 |-12 -12 Step 3 Write the row operation you will use to make the first nonzero entry in each row equal to 1. Multiply Row 1 by 1/2 and Row 2 by |× . Perform the operation and write the equivalent matrix. 1/2 R1+ X R2 →
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