PYQs Based Test - 01 : Matrix Algebra and System of Linear Equati..

Let M⁴ = I, (where I denotes the identity matrix) and M ≠ I, M² ≠ I and M³ ≠ I. Then, for any natural number k, M⁻¹ equals:

Consider the system of equations ≤ft[ {*20c 1&3&2\\ 2&2& - 3\\ 4&4& - 6\\ 2&5&2 } ]≤ft[ {*20c x_1\\ x_2\\ x_3 } ] = ≤ft[ {*20c 1\\ 1\\ 2\\ 1 } ] The value of x₃ (round off to the nearest integer), is ______.

Let A be a 10 × 10 matrix such that A⁵ is a null matrix, and let I be the 10 × 10 identity matrix. The determinant of A + I is ______.

The set of equations

x + y + z = 1

ax – ay + 3z = 5

5x – 3y + az = 6

has infinite solutions, if a =

Consider the matrix $P=\left[\begin{array}{ccc}\frac{1}{\sqrt{2}}& 0& \frac{1}{\sqrt{2}}\\ 0& 1& 0\\ \frac{-1}{\sqrt{2}}& 0& \frac{1}{\sqrt{2}}\end{array}\right]$

Which one of the following statements about P is INCORRECT?