Chapter 11: Q. 72 (page 756)

Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places.
$\{\begin{cases} 25 x + 61 y - 12 z = 15 \\ 18 x - 12 y + 7 z = - 3 \\ 3 x + 4 y - z = 12 \end{cases}$

Short Answer

Expert verified

On solving the system of equations, we get,

$x = 4.56, y = - 6, z = - 22.56$

Step by step solution

Step 1. Given information.

Consider the given question,

$\{\begin{cases} 25 x + 61 y - 12 z = 15 \\ 18 x - 12 y + 7 z = - 3 \\ 3 x + 4 y - z = 12 \end{cases}$

Step 2. Assume the equations.

Consider the given question and assume,

$A = [\begin{matrix} 25 & 61 & - 12 \\ 18 & - 12 & 7 \\ 3 & 4 & - 1 \end{matrix}], X = [\begin{matrix} x \\ y \\ z \end{matrix}], B = [\begin{matrix} 15 \\ - 3 \\ 12 \end{matrix}]$

The original system of equations can be written compactly as the matrix equation. Then,

$A X = B . . . . . . (i)$

Step 3. Find the inverse matrix.

We need to find the inverse matrix of A,

$A^{- 1} = [\begin{matrix} - 0.02 & 0.02 & 0.41 \\ 0.06 & 0.02 & - 0.57 \\ 0.16 & 0.12 & - 2.05 \end{matrix}]$

Multiply each side of equation (i) by $A^{- 1}$ ,

$A^{- 1} (A X) = A^{- 1} B (A^{- 1} A) X = A^{- 1} B I_{3} X = A^{- 1} B X = A^{- 1} B . . . . . . (i i)$

Use equation (ii) to findX. This can be done using the graphing utility.

On enter the matrices A and B into a graphing utility, we get,

$x = 4.56, y = - 6, z = - 22.56$

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Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places.
$\{\begin{cases} 25 x + 61 y - 12 z = 15 \\ 18 x - 12 y + 7 z = - 3 \\ 3 x + 4 y - z = 12 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Assume the equations.

Step 3. Find the inverse matrix.

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Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places.25x+61y-12z=1518x-12y+7z=-33x+4y-z=12

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Assume the equations.

Step 3. Find the inverse matrix.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Pure Maths

Applied Mathematics

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places.
$\{\begin{cases} 25 x + 61 y - 12 z = 15 \\ 18 x - 12 y + 7 z = - 3 \\ 3 x + 4 y - z = 12 \end{cases}$