Solve the system

\left\{\begin{aligned}x-2 y+3 z= & 4 \\2 x+y-4 z= & 3 \\-3 x+4 y-z= & -2\end{aligned}\right.

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Our explanations are based on the best information we have, but they may not always be right or fit every situation.

Step 1:

We start with the augmented matrix of the system, which...

Step 2:

We apply elementary row transformations to obtain a sim...

Step 3:

The first transformation we apply is -2 times the first...

Step 4:

Next, we perform the operation of adding -2 times the f...

Step 5:

We continue by multiplying the second row by 1/5 and th...

Step 6:

After that, we subtract the second row from the third r...

Step 7:

Finally, we multiply the third row by -1/2.

Step 8:

We now have a new matrix that represents an equivalent ...

Step 9:

This system is easier to solve than the original system...

Step 10:

Therefore, the solution to the original system of equat...

Question: 8.3.9

We must first solve the associated equality for y:...

Question: 8.9.4

The determinant of the coefficient matrix is
[late...

Question: 8.9.5

We shall merely list the various determinants. You...

Question: 8.3.3

We replace each ≤ with = and then sketch the resul...

Question: 8.3.4

The first two inequalities are the same as those c...

Question: 8.3.5

Using properties of absolute values (listed on pag...

Question: 8.3.6

The graphs of x²+y²=16 and x+y=2 are the circle an...

Question: 8.3.7

An equation of the circle is x²+y²=5². Since the i...

Question: 8.9.1

We plan to use property 3 of the theorem on row an...

Question: 8.9.3

\left|\begin{array}{ccc}1 & 1 & 1 \...