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3 and 4 .Determinants and Matrices
medium
The number of solutions of the system of equations $2x + y - z = 7,\,\,x - 3y + 2z = 1,\,x + 4y - 3z = 5$ is
A
$3$
B
$2$
C
$1$
D
$0$
Solution
(d) $\Delta = \left| {\,\begin{array}{*{20}{c}}2&1&{ – 1}\\1&{ – 3}&2\\1&4&{ – 3}\end{array}\,} \right|$
$ = 2(9 – 8) – 1( – 3 – 2) – 1(4 + 3) = 7 – 7 = 0$
Hence, number of solutions is zero.
Standard 12
Mathematics
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