Matrices And Determinants Ques 16
Passage Based Problems
Passage
Let $a$, $b$ and $c$ be three real numbers satisfying
$\begin{bmatrix} a & b & c \end{bmatrix}$ $\begin{bmatrix} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \end{bmatrix}$ =$\begin{bmatrix} 0 & 0 & 0 \end{bmatrix} \quad $ …(i)
If the point $P(a, b, c)$, with reference to Eq. (i), lies on the plane $2 x+y+z=1$, then the value of $7 a+b+c$ is
(a) 0
(b) 12
(c) 7
(d) 6
Show Answer
Answer:
Correct Answer: 16.(d)
Solution:
Formula:
Properties of matrix multiplication:
- As $(a, b, c)$ lies on $2 x+y+z=1 \Rightarrow 2 a+b+c=1$
$ \begin{array}{lll} \Rightarrow & 2 a+6 a-7 a =1 \\ \Rightarrow & a =1, b=6, c=-7 \\ \therefore & 7 a+b +c=7+6-7=6 \end{array} $
BETA
