For which of following ordered pairs (μ, delta) system of linear equations x+2 y+3 z=1 ; 3 x+

English

Gujarati

Hindi

3 and 4 .Determinants and Matrices

hard

For which of the following ordered pairs $(\mu, \delta)$ the system of linear equations $x+2 y+3 z=1$ ; $3 x+4 y+5 z=\mu$ ; $4 x+4 y+4 z=\delta$ is inconsistent?

A

$(1,0)$

B

$(4,6)$

C

$(3,4)$

D

$(4,3)$

(JEE MAIN-2020)

Solution

$2 \times(\text { ii })-2 \times(i)-(\text { iii })$

$0=2 \mu-2-\delta$

$\Rightarrow \delta=2(\mu-1)$

Standard 12

Mathematics

Share

Similar Questions

The number of values of $k $ for which the system of equations $(k + 1)x + 8y = 4k,$ $kx + (k + 3)y = 3k – 1$ has infinitely many solutions, is

medium

(IIT-2002)

The roots of the equation $\left| {\,\begin{array}{*{20}{c}}x&0&8\\4&1&3\\2&0&x\end{array}\,} \right| = 0$ are equal to

easy

If $x = cy + bz,\,\,y = az + cx,\,\,z = bx + ay$ (where $x, y, z $ are not all zero) have a solution other than $x = 0$, $y = 0$, $z = 0$ then $a, b$ and $ c $ are connected by the relation

medium

(IIT-1978)

The determinant $\left| {\,\begin{array}{*{20}{c}}a&b&{a – b}\\b&c&{b – c}\\2&1&0\end{array}\,} \right|$ is equal to zero if $a,b,c$ are in

easy

For non zero, $a,b,c$ if $\Delta = \left| {\,\begin{array}{*{20}{c}}{1 + a}&1&1\\1&{1 + b}&1\\1&1&{1 + c}\end{array}} \right| = 0$, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = $

normal