Let A = [ * 20 c 1&2&3 2&0&5 0&2&1 ] and b = [ * 20 r 0 - 3 1 ] . Which of the following is true?

Let A = [ * 20 c 1&2&3 2&0&5 0&2&1 ] and b = [ * 20 r 0 - 3 1 ] .…

MCQ

Let $A =$$\left[ {\begin{array}{*{20}{c}}1&2&3\\2&0&5\\0&2&1\end{array}} \right]$ and $b =$$\left[ {\begin{array}{*{20}{r}}0\\{ - 3}\\1\end{array}} \right]$ . Which of the following is true?

✓
$Ax = b$ has a unique solution.
B
$Ax = b$ has exactly three solutions.
C
$Ax = b$ has infinitely many solutions.
D
$Ax = b$ is inconsistent.

✓

Answer

Correct option: A.

$Ax = b$ has a unique solution.

a
$|A| = 1(0 - 10) - 2(2 - 6)$ $= - 10 + 8 = - 2$

==> $| A | \ne 0$

==>unique solution

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