3 and 4 .Determinants and Matrices
easy

समीकरणों  ${x_2} - {x_3} = 1,\,\, - {x_1} + 2{x_3} =  - 2,$ ${x_1} - 2{x_2} = 3$ के हलों की संख्या है

A

$0$

B

$1$

C

$2$

D

अनन्त

Solution

(a) $D = \left| {\,\begin{array}{*{20}{c}}0&1&{ – 1}\\{ – 1\,\,\,}&0&{\,\,\,2}\\1&{ – 2\,\,\,}&{\,\,\,0}\end{array}\,} \right|\, = \,0$ $D = \left| {\,\begin{array}{*{20}{c}} 1&1&{ – 1}\\ { – 2\,\,\,}&0&{\,\,\,2}\\ 3&{ – 2\,\,\,}&{\,\,\,0} \end{array}\,} \right|\, = \,14 \Rightarrow {D_1} \ne 0$

$D = 0$ तथा ${D_1} \ne 0$, $\therefore $ निकाय असंगत है।

अत: इसका कोई  हल नहीं है।

Standard 12
Mathematics

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