Question

Math

Posted 5 months ago

```
$\bar{A}=\left(\begin{array}{llll|l}
1 & 2 & 3 & 4 & 1 \\
0 & 5 & 6 & 7 & 2 \\
0 & 0 & 8 & 9 & 3 \\
0 & 0 & 0 & 0 & a
\end{array}\right)$
a. unique solution
b. infinite number of solutions
c. no solutions
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 2

Notice that the last row of the matrix is $[0 \; 0 \; 0 \; 0 \; a]$. If $a = 0$, the last row becomes $[0 \; 0 \; 0 \; 0 \; 0]$, which indicates a row of zeros in the augmented matrix

step 3

A row of zeros in the augmented matrix implies that the system of equations is consistent if the other rows do not lead to a contradiction

step 4

Since the other rows do not lead to a contradiction and the matrix is in row echelon form, the system has infinitely many solutions

B

Key Concept

Row of zeros in augmented matrix

Explanation

A row of zeros in the augmented matrix indicates that the system is consistent and has infinitely many solutions if there are no contradictions in the other rows.

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