a)

b)

dublattm
2022-01-22
Answered

Solve the given system of equations, or else show that there is no solution.

a)${x}_{1}+2{x}_{2}-{x}_{3}=1$

$2{x}_{1}+{x}_{2}+{x}_{3}=1$

${x}_{1}-{x}_{2}+2{x}_{3}=1$

b)${x}_{1}+2{x}_{2}-{x}_{3}=-2$

$-2{x}_{1}-4{x}_{2}+2{x}_{3}=4$

$2{x}_{1}+4{x}_{2}-2{x}_{3}=-4$

a)

b)

You can still ask an expert for help

coolbananas03ok

Answered 2022-01-23
Author has **20** answers

Step 1

Consider the following system:

Solve the system

Write augmented matrix

From the last row, we got

Hence the system has no solution

Step 2

Consider the following syste:

Solve the system

Write the augmented matrix

From this, we get

Here,

So choose

Then

Hence the solution to the given system is

ocretz56

Answered 2022-01-24
Author has **16** answers

Step 1

Part A

The coefficient matrix is :

$A=\left[\begin{array}{ccc}1& 2& -1\\ 2& 1& 1\\ 1& -1& 2\end{array}\right]$

Now

$det\left(A\right)=\left[\begin{array}{ccc}1& 2& -1\\ 2& 1& 1\\ 1& -1& 2\end{array}\right]=1\times (2+1)-2\times (4-1)-1\times (-2-1)$

$\Rightarrow det\left(A\right)=3-6+3=0$

Since$det\left(A\right)=0$ , the matrix is not invertible and thus, has no solution.

Step 2

Part B:

The coefficient matrix is:

$A=\left[\begin{array}{ccc}1& 2& -1\\ -2& -4& 2\\ 2& 4& -2\end{array}\right]$

Now

$det\left(A\right)==\left[\begin{array}{ccc}1& 2& -1\\ -2& -4& 2\\ 2& 4& -2\end{array}\right]=1\times (8-8)-2\times (4-4)-1\times (-8+8)$

$\Rightarrow det\left(A\right)=0+0+0=0$

Since$det\left(A\right)=0$ , the matrix is not invertible and thus, has no solution.

Part A

The coefficient matrix is :

Now

Since

Step 2

Part B:

The coefficient matrix is:

Now

Since

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