If p{lambda ^4} + q{lambda ^3} + r{lambda ^2} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the identity $p{\lambda ^4} + q{\lambda ^3} + r{\lambda ^2} + s\lambda + t = \left| {\begin{array}{*{20}{c}}{{\lambda ^2} + 3\lambda }&{\lam

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(B) Given the identity $p{\lambda ^4} + q{\lambda ^3} + r{\lambda ^2} + s\lambda + t = \left| {\begin{array}{*{20}{c}}{{\lambda ^2} + 3\lambda }&{\lambda - 1}&{\lambda + 3}\{\lambda + 1}&{2 - \lambda }&{\lambda - 4}\{\lambda - 3}&{\lambda + 4}&{3\lambda }\end{array}} ight|$.Since this is an identity in $\lambda$,it holds true for all values of $\lambda$.To find the value of $t$,we substitute $\lambda = 0$ into the equation:$t = \left| {\begin{array}{*{20}{c}}0&{ - 1}&3\1&2&{ - 4}\{ - 3}&4&0\end{array}} ight|$.Expanding the determinant along the first row:$t = 0(0 - (-16)) - (-1)(0 - 12) + 3(4 - (-6))$$t = 0 + 1(-12) + 3(10)$$t = -12 + 30 = 18$.Thus,the value of $t$ is $18$.

If $p{\lambda ^4} + q{\lambda ^3} + r{\lambda ^2} + s\lambda + t = \left| {\begin{array}{*{20}{c}}{{\lambda ^2} + 3\lambda }&{\lambda - 1}&{\lambda + 3}\\{\lambda + 1}&{2 - \lambda }&{\lambda - 4}\\{\lambda - 3}&{\lambda + 4}&{3\lambda }\end{array}} \right|$,the value of $t$ is

Similar Questions

The matrix $A = \begin{bmatrix} a & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2 \end{bmatrix}$ is not invertible only if $a =$

If $D = \left| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \end{array} \right|$ for $x \neq 0, y \neq 0$,then $D$ is

If $q_1, q_2, q_3$ are roots of the equation $x^3 + 64 = 0$,then the value of $\left| \begin{array}{ccc} q_1 & q_2 & q_3 \\ q_2 & q_3 & q_1 \\ q_3 & q_1 & q_2 \end{array} \right|$ is

The solution$(s)$ of the equation $\left| \begin{matrix} x & a & b \\ a & x & a \\ b & b & x \end{matrix} \right| = 0$ is/are:

If $\left|\begin{array}{ccc}0 & ab^2 & ac^2 \\ a^2b & 0 & bc^2 \\ a^2c & b^2c & 0\end{array}\right|=m(abc)^k$, then $m+k=$ . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module