Explanation Given information: The given matrix A is [ 2 − 1 1 − 1 4 − 3 1 − 3 2 ] . Calculation: Use Gauss Jordan method. Write the given matrix with identity matrix. A = [ 2 − 1 1 − 1 4 − 3 1 − 3 2 | 1 0 0 0 1 0 0 0 1 ] (1) The vertical line in Equation (1) denotes the separation of two matrices. The first element in Equation (1) a 11 should be 1. Replace row 1 by dividing 2 with each element of row 1. A = [ 2 − 1 1 − 1 4 − 3 1 − 3 2 | 1 0 0 0 1 0 0 0 1 ] → R 1 → R 1 2 = [ 2 2 − 1 2 1 2 − 1 4 − 3 1 − 3 2 | 1 2 0 2 0 2 0 1 0 0 0 1 ] = [ 1 − 1 2 1 2 − 1 4 − 3 1 − 3 2 | 1 2 0 0 0 1 0 0 0 1 ] (2) The elements a 21 and a 31 in Equation (2) should be 0. Replace the elements of row 2 by adding each element of row 1 from the corresponding element in row 2 and Replace the elements of row 3 by subtracting element of row 1 from the corresponding element in row 3. A = [ 1 − 1 2 1 2 − 1 4 − 3 1 − 3 2 | 1 2 0 0 0 1 0 0 0 1 ] → R 2 = R 2 + R 1 R 3 = R 3 − R 1 = [ 1 − 1 2 1 2 − 1 + ( 1 ) 4 − 1 2 − 3 + 1 2 1 − 1 − 3 − ( − 1 2 ) 2 − 1 2 | 1 2 0 0 0 + 1 2 1 + 0 0 + 0 0 − 1 2 0 − 0 1 − 0 ] = [ 1 − 1 2 1 2 0 7 2 − 5 2 0 − 5 2 3 2 | 1 2 0 0 1 2 1 0 − 1 2 0 1 ] (3) The bottom row element a 22 in Equation (3) should be 1. Replace the row 2 by dividing 7 2 with each element in row 2. A = [ 1 − 1 2 1 2 0 7 2 − 5 2 0 − 5 2 3 2 | 1 2 0 0 1 2 1 0 − 1 2 0 1 ] → R 2 7 2 = [ 1 − 1 2 1 2 0 7 2 7 2 7 2 − 5 2 7 2 0 − 5 2 3 2 | 1 2 0 0 1 2 7 2 1 7 2 0 7 2 − 1 2 0 1 ] = [ 1 − 1 2 1 2 0 1 − 5 7 0 − 5 2 3 2 | 1 2 0 0 1 7 2 7 0 − 1 2 0 1 ] (4) The elements a 12 and a 32 in Equation (4) should be zero. Replace the elements of row 1 by subtracting 1 2 times each element of row 2 from the corresponding element in row 1. Replace the elements of row 3 by adding 5 2 times each element of row 2 from the corresponding element in row 3

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Chapter 16.3, Problem 40E

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Chapter 16.3, Problem 39E

Chapter 16.3, Problem 41E

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Chapter 16 Solutions

Basic Technical Mathematics

Ch. 16.1 - For matrices A and B, find A + B. Ch. 16.1 - Prob. 2PE Ch. 16.1 - Prob. 3PE Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E

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Chapter 16 Solutions