If the system of linear equations
2x + y $-$ z = 7
x $-$ 3y + 2z = 1
x + 4y + $\delta$z = k, where $\delta$, k $\in$ R has infinitely many solutions, then $\delta$ + k is equal to:
Solution
<p>$2x + y - z = 7$</p>
<p>$x - 3y + 2z = 1$</p>
<p>$x + 4y + \delta z = k$</p>
<p>$$\Delta = \left| {\matrix{
2 & 1 & { - 1} \cr
1 & { - 3} & 2 \cr
1 & 4 & \delta \cr
} } \right| = - 7\delta - 21 = 0$$</p>
<p>$\delta = - 3$</p>
<p>$${\Delta _1} = \left| {\matrix{
7 & 1 & { - 1} \cr
1 & { - 3} & 2 \cr
k & 4 & { - 3} \cr
} } \right|$$</p>
<p>$\Rightarrow 6 - k = 0 \Rightarrow k = 6$</p>
<p>$\delta + k = - 3 + 6 = 3$</p>
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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