Q4E Find the matrix of linear transf... [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 2: Q4E (page 53)

Find the matrix of linear transformation.
$y_{1} = 9 x_{1} + 3 x_{2} + 3 x_{3} y_{2} = 2 x_{1} - 9 x_{2} + x_{3} y_{3} = 4 x_{1} - 9 x_{2} - 2 x_{3} y_{4} = 5 x_{1} + x_{2} + 5 x_{3}$

Short Answer

Expert verified

Matrix representation of given system is $A = [\begin{matrix} 9 & 3 & 3 \\ 2 & - 9 & 1 \\ 4 & - 9 & - 2 \\ 5 & 1 & 5 \end{matrix}]$ .

Step by step solution

Step 1: System of equation

We have given the linear transformation is $y_{1} {= 9x}_{1} + 3 x_{2} + 3 x_{3} y_{2} {= 2x}_{1} {- 9x}_{2} {+x}_{3} y_{3} {= 4x}_{1} - 9 x_{2} - 2 x_{3} y_{4} = 5 x_{1} + x_{2} + 5 x_{3}$ .

Matrix for linear transformation

The given system is, $y_{1} {= 9x}_{1} + 3 x_{2} + 3 x_{3} y_{2} {= 2x}_{1} {- 9x}_{2} {+x}_{3} y_{3} {= 4x}_{1} - 9 x_{2} - 2 x_{3} y_{4} = 5 x_{1} + x_{2} + 5 x_{3}$ .

As there are four equations and three unknowns, so the order of the matrix will be $4 脳 3$

Let this $4 脳 3$ matrix represented byA which will be the coefficient matrix.

$A = [\begin{matrix} 9 & 3 & 3 \\ 2 & - 9 & 1 \\ 4 & - 9 & - 2 \\ 5 & 1 & 5 \end{matrix}]$

Hence, matrix representation of the given system is $A = [\begin{matrix} 9 & 3 & 3 \\ 2 & - 9 & 1 \\ 4 & - 9 & - 2 \\ 5 & 1 & 5 \end{matrix}]$ .

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91影视

Find the matrix of linear transformation.
$y_{1} = 9 x_{1} + 3 x_{2} + 3 x_{3} y_{2} = 2 x_{1} - 9 x_{2} + x_{3} y_{3} = 4 x_{1} - 9 x_{2} - 2 x_{3} y_{4} = 5 x_{1} + x_{2} + 5 x_{3}$

Short Answer

Step by step solution

Step 1: System of equation

Matrix for linear transformation

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91影视

Find the matrix of linear transformation.y1=9x1+3x2+3x3y2=2x1-9x2+x3y3=4x1-9x2-2x3y4=5x1+x2+5x3

Short Answer

Step by step solution

Step 1: System of equation

Matrix for linear transformation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Pure Maths

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Find the matrix of linear transformation.
$y_{1} = 9 x_{1} + 3 x_{2} + 3 x_{3} y_{2} = 2 x_{1} - 9 x_{2} + x_{3} y_{3} = 4 x_{1} - 9 x_{2} - 2 x_{3} y_{4} = 5 x_{1} + x_{2} + 5 x_{3}$