Skip to main content
Yukti Vault

Determinant - JEE Mathematics question (JEE Advanced 2021 Paper 1)

Comprehension · Questions 1–1

Read the passage given below and answer the questions that follow.

Let $\alpha,\beta$ and $\gamma$ be real numbers such that the system of linear equations $$x+2y+3z=\alpha$$ $$4x+5y+6z=\beta$$ $$7x+8y+9z=\gamma-1$$ is consistent. Let $|M|$ represent the determinant of the matrix $$M=\begin{bmatrix}\alpha&2&\gamma\\ \beta&1&0\\ -1&0&1\end{bmatrix}$$ Let $P$ be the plane containing all those $(\alpha,\beta,\gamma)$ for which the above system of linear equations is consistent, and $D$ be the square of the distance of the point $(0,1,0)$ from the plane $P$.
JEE Advanced 2021 Paper 1Question 1
The value of $|M|$ is ___ .
Determinant

Answer$1$

Solution

Consistency: row$_1-2$row$_2+$row$_3$ gives $\alpha-2\beta+\gamma-1=0$. $|M|=\alpha(1)-2(\beta)+\gamma(1)=\alpha-2\beta+\gamma=1$.

More from Determinant