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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
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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