Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equationAx = b. Then solve the system and write the solution as a vector.Write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b.A =16-2 -53- 5H3 b= 42 6- 214

We have given a matrix equation .where A and b are:Solution vector is Solution can be obtained by…

Answered: Given A and b to the right, write the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation
Ax = b. Then solve the system and write the solution as a vector.
Write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b.
A =
1
6
-2 -5
3
- 5
H
3 b= 4
2 6
- 2
14

Expert Solution

Step 1: Description of given data and augmented matrix:

We have given a matrix equation $A x equals b$ .

where A and b are:

$A equals open square brackets table row 1 6 cell negative 5 end cell row cell negative 2 end cell cell negative 5 end cell 3 row 3 2 6 end table close square brackets comma space b equals open square brackets table row cell negative 2 end cell row 4 row 14 end table close square brackets$

Solution vector is $X with rightwards arrow on top equals open square brackets table row cell x subscript 1 end cell row cell x subscript 2 end cell row cell x subscript 3 end cell end table close square brackets$

Solution can be obtained by using $A x equals b$

That is, $open square brackets table row 1 6 cell negative 5 end cell row cell negative 2 end cell cell negative 5 end cell 3 row 3 2 6 end table close square brackets open square brackets table row cell x subscript 1 end cell row cell x subscript 2 end cell row cell x subscript 3 end cell end table close square brackets equals open square brackets table row cell negative 2 end cell row 4 row 14 end table close square brackets$

Now, the augmented matrix written as:

$open square brackets table row 1 6 cell negative 5 end cell cell negative 2 end cell row cell negative 2 end cell cell negative 5 end cell 3 4 row 3 2 6 14 end table close square brackets$