Q24E Use Cramer's rule to solve the s... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 6: Q24E (page 307)

Use Cramer's rule to solve the systems in Exercises 22 through 24.
24. $| \begin{matrix} 2 x + 3 y & = 8 \\ 4 y + 5 z & = 3 \\ 6 x + 7 z & = - 1 \end{matrix} |$

Short Answer

Expert verified

Therefore

$x = [\begin{matrix} 1 \\ 2 \\ - 1 \end{matrix}]$

Step by step solution

Definition.

In matrices, Cramer's rule expresses the solution in terms of the determinants of the coefficient matrix (i.e., for a square matrix) and of matrices obtained from it by replacing one column by the column vector of right-hand-sides of the equations.

To solve.

Using Cramer's rule, we solve:

$\det A = |\begin{matrix} 2 & 3 & 0 \\ 0 & 4 & 5 \\ 6 & 0 & 7 \end{matrix}| \det A = 146 x_{1} = \frac{|\begin{matrix} 8 & 3 & 0 \\ 3 & 4 & 5 \\ - 1 & 0 & 7 \end{matrix}|}{146} x_{1} = \frac{146}{146} x_{1} = 1$

$x_{2} = \frac{|\begin{matrix} 2 & 8 & 0 \\ 0 & 3 & 5 \\ 6 & - 1 & 7 \end{matrix}|}{146} x_{2} = 2 x_{3} = \frac{|\begin{matrix} 2 & 3 & 8 \\ 0 & 4 & 3 \\ 6 & 0 & - 1 \end{matrix}|}{146} x_{3} = \frac{- 146}{146} x_{3} = - 1$

Therefore,

$x = [\begin{matrix} 1 \\ 2 \\ - 1 \end{matrix}]$

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91影视

Use Cramer's rule to solve the systems in Exercises 22 through 24.
24. $| \begin{matrix} 2 x + 3 y & = 8 \\ 4 y + 5 z & = 3 \\ 6 x + 7 z & = - 1 \end{matrix} |$

Short Answer

Step by step solution

Definition.

To solve.

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91影视

Use Cramer's rule to solve the systems in Exercises 22 through 24.24. |2x+3y=84y+5z=36x+7z=-1|

Short Answer

Step by step solution

Definition.

To solve.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Use Cramer's rule to solve the systems in Exercises 22 through 24.
24. $| \begin{matrix} 2 x + 3 y & = 8 \\ 4 y + 5 z & = 3 \\ 6 x + 7 z & = - 1 \end{matrix} |$