BITSAT 2024 | Matrices and Determinants Question 2 | Mathematics

Suppose $ p, q, r \neq 0 $ and system of equation $ (p+a) x+b y+c z=0 $, $ a x+(q+b) y+c z=0 $, $ a x+b y+(r+c) z=0 $, has a non-trivial solution, then the value of $ \frac{a}{p}+\frac{b}{q}+\frac{c}{r} $ is

-1

BITSAT 2024

MCQ (Single Correct Answer)

-1

If matrix $ A=\left[\begin{array}{ccc}3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1\end{array}\right] $ and $ A^{-1}=\frac{1}{k} \operatorname{adj}(A) $,

-7

-11

BITSAT 2023

MCQ (Single Correct Answer)

-1

If the system of linear equation $$3 x-2 y+z=2, 4 x-3 y+3 z=-5$$ and $$7 x-5 y+\lambda z=9$$ has no solution, then $$\lambda$$ equals to

BITSAT 2023

MCQ (Single Correct Answer)

-1

Let $$A=\left[\begin{array}{lll}3 & 2 & 3 \\ 4 & 1 & 0 \\ 2 & 5 & 1\end{array}\right]$$ and $$49 B=\left[\begin{array}{ccc}1 & 13 & -3 \\ -4 & -3 & 12 \\ \alpha & -11 & -5\end{array}\right]$$ If $$B$$ is the inverse of $$A$$, then the value of $$\alpha$$ is

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