Explanation Approach: Conversion of the augmented matrix into diagonal form: STEP 1: Obtaining 1 as the first element of the first column. STEP 2: Using the first row, the remaining entries in the first column are made zero. STEP 3: Obtaining 1 as the second element of the second column. STEP 4: Using the second row, the remaining entries in the second column are made zero. Hence, containing in the above manner the last matrix obtained should be of the form [ A diagonal matrix | A column matrix ] From the above obtained form of the matrix, the solution for the given system can be obtained. CASE 1: Consistent – Single solution A diagonal matrix in the left of the vertical line and any real value in the right of the vertical line against the rows of the diagonal matrix – Consistent and Single solution. CASE 2: Inconsistent – No solution. Any one of the row to the left of the vertical line become zero and a non - zero entry in the right of the vertical line against the zero row in the left – Inconsistent – No solution. CASE 3: Consistent – Infinitely many solution Any one of the row to the left of the vertical line become zero and also the entry in the right of the vertical line against the zero row in the left – Consistent – Infinitely many solution. Matrix Row Transformation: For any augmented matrix of a system of linear equations, the following row transformations interchange any two rows. Multiply or divide the elements of any row by a nonzero real number. Replace any row of the matrix by the sum of the elements of that row and a multiple of the elements of another row. Calculation: Given, { 3 x − y = − 4 − 6 x + 2 y = 8 The above two equations are having its variable terms in the left and the constant terms in the right. Hence, the augmented matrix is given by, [ 3 − 1 − 4 − 6 2 8 ] The first entry of the first column in the above matrix is not 1. Divide the first row by 3

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Author: Gustafson

Publisher: CENGAGE L

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Chapter 6.CR, Problem 22E

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The system { 3x−y=−4−6x+2y=8 by matrix method, if possible.

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Chapter 6.CR, Problem 21E

Chapter 6.CR, Problem 23E

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