Home Courses Contact About

6. ⇒ (MHT CET 2021 21th September Evening Shift )

If $A = [\begin{array}{ccc} \cos θ & - \sin θ & 0 \\ \sin θ & \cos θ & 0 \\ 0 & 0 & 1 \end{array}]$ , then $adj A =$

A. $[\begin{array}{ccc} - \cos θ & - \sin θ & 0 \\ \sin θ & \cos θ & 0 \\ 0 & 0 & 1 \end{array}]$

B. $[\begin{array}{ccc} \cos θ & \sin θ & 0 \\ \sin θ & \cos θ & 0 \\ 0 & 0 & 1 \end{array}]$

C. $[\begin{array}{ccc} \cos θ & \sin θ & 0 \\ - \sin θ & \cos θ & 0 \\ 0 & 0 & 1 \end{array}]$

D. $[\begin{array}{ccc} \cos θ & - \sin θ & 0 \\ \sin θ & \cos θ & 0 \\ 0 & 0 & 1 \end{array}]$

Correct answer option is (C)

$\begin{aligned} A = [\begin{array}{ccc} \cos θ & - \sin θ & 0 \\ \sin θ & \cos θ & 0 \\ 0 & 0 & 1 \end{array}] \\ ∴ adj A = {[\begin{array}{ccc} \cos θ & - \sin θ & 0 \\ \sin θ & \cos θ & 0 \\ 0 & 0 & 1 \end{array}]}^{T} = [\begin{array}{ccc} \cos θ & \sin θ & 0 \\ - \sin θ & \cos θ & 0 \\ 0 & 0 & 1 \end{array}] \end{aligned}$

7. ⇒ (MHT CET 2021 21th September Morning Shift )

If $A = [\begin{array}{ccc} 1 & 0 & 2 \\ - 1 & 1 & - 2 \\ 0 & 2 & 1 \end{array}], adj A = [\begin{array}{ccc} 5 & x & - 2 \\ 1 & 1 & 0 \\ - 2 & - 2 & y \end{array}]$ , then value of $x + y$ is

A. 6

B. 3

C. 4

D. 5

Correct answer option is (D)

$x$ is element $a_{12}$ in $adj (A)$ .

$∴ x =$ cofactor of $a_{21} = (- 1)^{2 + 1} | \begin{array}{ll} 0 & 2 \\ 2 & 1 \end{array} | = - (- 4) = 4$

Similarly $y = (- 1)^{3 + 3} | \begin{array}{cc} 1 & 0 \\ - 1 & 1 \end{array} | = 1 \Rightarrow x + y = 5$

⇒Matrices