PYQs Based test 26: Engineering Mathematics

Consider a 2 × 2 matrix M = ≤ft[ {*20c v_1&v_2 } ], where, v₁ and v₂ are the column vectors. Suppose M^ - 1 = ≤ft[ {*20c u_1^T\\ u_2^T } ], where u${}^T$ ₁ and u${}^T$ ₂ are the row vectors. Consider the following statements.

Statement: u${}^T$ ₁v₁ = 1 and u${}^T$ ₂v₂ = 1

Statement: u${}^T$ ₁v₂ = 0 and u${}^T$ ₂v₁ = 0

Which of the following options is correct?

Consider a signal defined by

x≤ft( t ) = ≤ft\{ {*20c {e^~j10t}&for≤ft| t | ≤ 1\\ 0&for≤ft| t | > 1 } .

Its Fourier Transform is

The volume enclosed by the surface $f\left(x,y\right)=e^x$ over the triangle bounded by the line $x=y;x=0;y=1$ in the xy plane is ________.

Two players, $A$ and $B$, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $A$ starts the game, the probability that $A$ wins the game is

Let $A$ be a $4\times 3$ real matrix with rank 2. Which one of the following statement is TRUE?