Explanation Given information: The given equations are, 2 x + 2 t = 0 3 x + y + z = − 1 2 y − z + 3 t = 1 2 z − 3 t = 1 Calculation: Write the given equations in general matrix form [ A ] . [ A ] = [ 2 0 0 2 3 1 1 0 0 2 − 1 3 0 0 2 − 3 ] Find the determinant | A | of matrix A . | A | = | 2 0 0 2 3 1 1 0 0 2 − 1 3 0 0 2 − 3 | Expand matrix A by first column. | A | = 2 | 1 1 0 2 − 1 3 0 2 − 3 | − 3 | 0 0 2 2 − 1 3 0 2 − 3 | + 0 − 0 = 2 [ 1 ( 3 − 6 ) − 2 ( − 3 ) + 0 ] − 3 [ 0 − 0 + 2 ( 4 − 0 ) ] = 2 ( − 3 + 6 ) − 3 ( 8 ) = 6 − 24 = − 18 Replace the coefficients of x (elements of column 1) with constant [ X ] to form matrix [ X A ] . [ X A ] = [ 0 0 0 2 − 1 1 1 0 1 2 − 1 3 1 0 2 − 3 ] Find the determinant | X A | of matrix X A . | X A | = | 0 0 0 2 − 1 1 1 0 1 2 − 1 3 1 0 2 − 3 | Expand matrix X A by first row. | X A | = 0 − 0 + 0 − 2 | − 1 1 1 1 2 − 1 1 0 2 | = − 2 [ ( − 1 ) ( 4 − 0 ) − 1 ( 2 + 1 ) + 1 ( 0 − 2 ) ] = − 2 ( − 4 − 3 − 2 ) = 18 Find the value of x using the equation: x = | X A | | A | Substitute 18 for | X A | and − 18 for | A | . x = 18 − 18 = − 1 Therefore, value of x is − 1 _ . Replace the coefficients of y (elements of column 2) with constant [ X ] to form matrix [ X B ] . [ X B ] = [ 2 0 0 2 3 − 1 1 0 0 1 − 1 3 0 1 2 − 3 ] Find the determinant | X B | of matrix X B . | X B | = | 2 0 0 2 3 − 1 1 0 0 1 − 1 3 0 1 2 − 3 | Expand matrix X B by first column. | X B | = 2 | − 1 1 0 1 − 1 3 1 2 − 3 | − 3 | 0 0 2 1 − 1 3 1 2 − 3 | + 0 − 0 = 2 [ ( − 1 ) ( 3 − 6 ) − 1 ( − 3 − 3 ) + 0 ] − 3 [ 0 − 0 + 2 ( 2 + 1 ) ] = 2 ( 3 + 6 ) − 3 ( 6 ) = 0 Find the value of y using the equation: y = | X B | | A | Substitute 0 for | X B | and − 18 for | A |

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 16.6, Problem 21E

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Chapter 16.6, Problem 20E

Chapter 16.6, Problem 22E

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Chapter 16 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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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