PYQ Vault
EbooksTutor

Matrix satisfying A^T = alpha A + beta I: take the transpose again

This type of question, asked 2 times: 30 Jan 2023, 11 Apr 2023. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    30 Jan 2023

    161
    If PP is a 3×33 \times 3 real matrix such that PT=aP+(a−1)IP^{T}= aP + (a - 1)I, where a>1a > 1, then

    Tap an option to check your answer.

  2. Question 2

    11 Apr 2023

    76
    Let AA be a 2×22 \times 2 matrix with real entries such that A′=αA+IA^{'}= \alpha A + I, where α∈R−{−1,1}\mathbf{\alpha \in R - \{ - 1,1\}}. If det⁡\det (A2−A)=4\left( A^{2}- A \right)= 4, then the sum of all possible values of α\alpha is equal to

    Tap an option to check your answer.