Explanation Given information: The linear system of equations is, { − 2 a + c = 2 a + 2 b − c = 9 3 a + 5 b + 2 c = 22 Formula used : The general linear system of equations can be expressed as, { a 11 x + a 12 y + a 13 z = r a 21 x + a 22 y + a 23 z = s a 31 x + a 32 y + a 33 z = t The solution of the above system of equation can be calculated as, x = | D x | | D | , y = | D y | | D | and z = | D z | | D | Here, the determinant | D | = | a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 | ≠ 0 . The matrices D , D x , D y and D z are represented as follows, D = [ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ] , D x = [ r a 12 a 13 s a 22 a 23 t a 32 a 33 ] D y = [ a 11 r a 13 a 21 s a 23 a 31 t a 33 ] and D z = [ a 11 a 12 r a 21 a 22 s a 31 a 32 t ] Calculation: The system of equations is { − 2 a + c = 2 a + 2 b − c = 9 3 a + 5 b + 2 c = 22 . For the system of equations, the coefficient matrix can be obtained as, D = [ 5 − 3 1 0 4 − 6 7 10 0 ] The determinant of the coefficient matrix D can be calculated as, | D | = | − 2 0 1 1 2 − 1 3 5 2 | = − 2 ( 2 ⋅ 2 − ( − 1 ) ⋅ 5 ) + 0 ( 1 ⋅ 2 − ( − 1 ) ⋅ 3 ) + 1 ( 1 ⋅ 5 − 2 ⋅ 3 ) = − 2 ( 4 + 5 ) + 0 + 1 ( 5 − 6 ) = − 19 The matrix D a can be obtained by replacing the first column of the matrix by the values of the equations or the constants 2 , 9 , 22 as, D a = [ 2 0 1 9 2 − 1

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 6.4, Problem 50E

To determine

To solve:

The system of equations {−2a+c=2a+2b−c=93a+5b+2c=22 by the Cramer’s rule.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 49E

Chapter 6.4, Problem 51E

Students have asked these similar questions

How long is a guy wire reaching from the top of a 15-foot pole to a point on the ground 9-feet from the pole? Question content area bottom Part 1 The guy wire is exactly feet long. (Type an exact answer, using radicals as needed.) Part 2 The guy wire is approximatelyfeet long. (Round to the nearest thousandth.)

Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w k

Consider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]

Chapter 6 Solutions

College Algebra

Ch. 6.1 - If a system of linear equations has infinitely...Ch. 6.1 - Write the augmented matrix of the following system...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Dimension of a Matrix State the dimension of the...Ch. 6.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The system of equations { − 2 a + c = 2 a + 2 b − c = 9 3 a + 5 b + 2 c = 22 by the Cramer’s rule.

Solution Summary: The author explains how the linear system of equations is solved by the Cramer's rule.

Videos

To solve:

The system of equations {−2a+c=2a+2b−c=93a+5b+2c=22 by the Cramer’s rule.

Want to see the full answer?

Chapter 6 Solutions

The system of equations { − 2 a + c = 2 a + 2 b − c = 9 3 a + 5 b + 2 c = 22 by the Cramer’s rule.

Solution Summary: The author explains how the linear system of equations is solved by the Cramer's rule.

Videos

To solve: The system of equations {−2a+c=2a+2b−c=93a+5b+2c=22 by the Cramer’s rule.

Want to see the full answer?

Chapter 6 Solutions

To solve:

The system of equations {−2a+c=2a+2b−c=93a+5b+2c=22 by the Cramer’s rule.