Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

If $B=\begin{bmatrix} 5 &2\alpha &1 \\ 0 &2 &1 \\ \alpha &3 &-1 \end{bmatrix}$ is the inverse of a $3\times 3$ matrix A, then the sum of all values of $\alpha$ for which det $\left ( A \right )+1=0,$ is :

Option 1)
$0$

Option 2)
$1$

Option 3)
$2$

Option 4)
$-1$

Answers (2)

$B=\begin{bmatrix} 5 &2\alpha &1 \\ 0 &2 &1 \\ \alpha & 3 &-1 \end{bmatrix}$

$\left | B \right |=5\left ( -5 \right )-2\alpha \left ( -\alpha \right )-2\alpha$

$=2\alpha ^{2}-2\alpha -25$

$1+\left | A \right |=2\alpha ^{2}-2\alpha -25+1=0$

$=2\alpha ^{2}-2\alpha -24=0$

$=\alpha ^{2}-\alpha -12=0$

$=\alpha ^{2}-4\alpha +3\alpha -12=0$

$=\left ( \alpha -4 \right )\left ( \alpha +3 \right )=0$

$root=$ $4,-3$

$sum\: \: of\: \: root=4-3$

$=1$

Option 1)

$0$

Option 2)

$1$

Option 3)

$2$

Option 4)

$-1$

Posted by

Vakul

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

2

Posted by

Noor fathima

View full answer

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 Registration LIVE: NTA session 1 applications close today for BTech, BArch aspirants

anam-khan

Parliamentary panel to review mushrooming of coaching centres, PM SHRI schools, HECI plans

anam-khan

JEE Main 2026 Registration LIVE: NTA to close session 1 application tomorrow; from correction on December 1, 2

Latest Question