If system of equations, x + 2y - 3z = 1 , (k + 3)z = 3, (2k + 1)x + z = 0 is inconsistent, then valu

English

Gujarati

Hindi

3 and 4 .Determinants and Matrices

medium

If the system of equations, $x + 2y - 3z = 1$, $(k + 3)z = 3,$ $(2k + 1)x + z = 0$is inconsistent, then the value of $ k$ is

$-3$

$1/2$

$0$

$2$

Solution

(a) For the equation to be inconsistent $D = 0$
$\therefore $$D = \left| {\,\begin{array}{*{20}{c}}1&2&{ – 3}\\0&0&{k + 3}\\{2k + 1}&0&1\end{array}\,} \right| = 0 \Rightarrow k = – 3$
and ${D_1} = \left| {\,\begin{array}{*{20}{c}}1&2&{ – 3}\\3&0&0\\0&0&1\end{array}\,} \right| \ne 0$
So that system is inconsistent for $k = – 3$.

Standard 12

Mathematics

In a $\Delta ABC,$ if $\left| {\,\begin{array}{*{20}{c}}1&a&b\\1&c&a\\1&b&c\end{array}\,} \right| = 0$, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C = $

hard

If the system of linear equations $2x + 2y + 3z = a$ ; $3x – y + 5z = b$ ; $x – 3y + 2z = c$ Where $a, b, c$ are non zero real numbers, has more than one solution, then

hard

(JEE MAIN-2019)

If $\left| {\,\begin{array}{*{20}{c}}{3x – 8}&3&3\\3&{3x – 8}&3\\3&3&{3x – 8}\end{array}\,} \right| = 0,$ then the values of $x$ are

hard

Find equation of line joining $(3,1)$ and $(9,3)$ using determinants

easy

The least value of the product $xyz$ for which the determinant $\left| {\begin{array}{*{20}{c}}
x&1&1 \\
1&y&1 \\
1&1&z
\end{array}} \right|$ is non-negative, is

hard

(JEE MAIN-2015)

If the system of equations, $x + 2y - 3z = 1$, $(k + 3)z = 3,$ $(2k + 1)x + z = 0$is inconsistent, then the value of $ k$ is

Solution

Similar Questions

In a $\Delta ABC,$ if $\left| {\,\begin{array}{*{20}{c}}1&a&b\\1&c&a\\1&b&c\end{array}\,} \right| = 0$, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C = $

If the system of linear equations $2x + 2y + 3z = a$ ; $3x – y + 5z = b$ ; $x – 3y + 2z = c$ Where $a, b, c$ are non zero real numbers, has more than one solution, then

If $\left| {\,\begin{array}{*{20}{c}}{3x – 8}&3&3\\3&{3x – 8}&3\\3&3&{3x – 8}\end{array}\,} \right| = 0,$ then the values of $x$ are

Find equation of line joining $(3,1)$ and $(9,3)$ using determinants

The least value of the product $xyz$ for which the determinant $\left| {\begin{array}{*{20}{c}} x&1&1 \\ 1&y&1 \\ 1&1&z \end{array}} \right|$ is non-negative, is

Start a Free Trial Now

The least value of the product $xyz$ for which the determinant $\left| {\begin{array}{*{20}{c}}
x&1&1 \\
1&y&1 \\
1&1&z
\end{array}} \right|$ is non-negative, is