Q. 21 In Problems 20鈥�25, solve each ... [FREE SOLUTION]

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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 21 (page 793)

In Problems 20鈥�25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 5 x 鈭� 6 y 鈭� 3 z = 6 \\ 4 x 鈭� 7 y 鈭� 2 z = 鈭� 3 \\ 3 x + y 鈭� 7 z = 1 \end{cases}$

Short Answer

Expert verified

The solutions to the given equation are $x = \frac{33}{4}, y = \frac{25}{6}, z = \frac{41}{12}$

Step by step solution

Step 1. Given information

The given system of equations is $\{\begin{cases} 5 x 鈭� 6 y 鈭� 3 z = 6 \\ 4 x 鈭� 7 y 鈭� 2 z = 鈭� 3 \\ 3 x + y 鈭� 7 z = 1 \end{cases}$

Step 2. Solve system of equations using matrix

$A = [\begin{array}{ccc} 5 & 鈭� 6 & 鈭� 3 \\ 4 & 鈭� 7 & 鈭� 2 \\ 3 & 1 & 鈭� 7 \end{array}], X = [\begin{array}{l} x \\ y \\ z \end{array}], B = [\begin{matrix} 6 \\ 鈭� 3 \\ 5 \end{matrix}]$

$A X = B X = A^{- 1} B$

The inverse of the matrix $A$ can now be determined by using the graphical utility.

So,

$A^{- 1} = [\begin{array}{ccc} \frac{17}{16} & 鈭� \frac{15}{16} & 鈭� \frac{3}{16} \\ \frac{11}{24} & 鈭� \frac{13}{24} & 鈭� \frac{1}{24} \\ \frac{25}{48} & 鈭� \frac{23}{48} & 鈭� \frac{11}{48} \end{array}]$

$X = A^{- 1} B \begin{aligned} X & = [\begin{array}{c} 6 \\ 鈭� 3 \\ 5 \end{array}] [\begin{array}{ccc} \frac{17}{16} & 鈭� \frac{15}{16} & 鈭� \frac{3}{16} \\ \frac{11}{24} & 鈭� \frac{13}{24} & 鈭� \frac{1}{24} \\ \frac{25}{48} & 鈭� \frac{23}{48} & 鈭� \frac{11}{48} \end{array}] \\ = [\begin{matrix} 6 脳 \frac{17}{16} + (鈭� 3) 脳 (鈭� \frac{15}{16}) + 5 脳 (鈭� \frac{3}{16}) \\ 6 脳 \frac{11}{24} + (鈭� 3) 脳 (鈭� \frac{13}{24}) + 5 脳 (鈭� \frac{1}{24}) \\ 6 脳 \frac{25}{48} + (鈭� 3) 脳 (鈭� \frac{23}{48}) + 5 脳 (鈭� \frac{11}{48}) \end{matrix}] \\ = [\begin{matrix} \frac{102}{16} + \frac{45}{16} 鈭� \frac{15}{16} \\ \frac{66}{24} + \frac{39}{24} 鈭� \frac{5}{24} \\ \frac{150}{48} + \frac{69}{48} 鈭� \frac{55}{48} \end{matrix}] \\ = [\begin{matrix} \frac{33}{4} \\ \frac{25}{6} \\ \frac{41}{12} \end{matrix}] \end{aligned}$

The solutions to the given equation are $x = \frac{33}{4}, y = \frac{25}{6}, z = \frac{41}{12}$

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91影视

In Problems 20鈥�25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 5 x 鈭� 6 y 鈭� 3 z = 6 \\ 4 x 鈭� 7 y 鈭� 2 z = 鈭� 3 \\ 3 x + y 鈭� 7 z = 1 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve system of equations using matrix

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

In Problems 20鈥�25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.5x鈭�6y鈭�3z=64x鈭�7y鈭�2z=鈭�33x+y鈭�7z=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve system of equations using matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Calculus

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 20鈥�25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 5 x 鈭� 6 y 鈭� 3 z = 6 \\ 4 x 鈭� 7 y 鈭� 2 z = 鈭� 3 \\ 3 x + y 鈭� 7 z = 1 \end{cases}$