Q32Single correct2 Marks7 Aug 2022

Which of the following option is/are true?

A

If L and L' are two affine subspaces of $\mathbb{R}^3$, then L cap L' is an affine subspace of $\mathbb{R}^3$.

B

Let Ax = b be a system of linear equations with infinitely many solutions and let P be an invertible matrix such that product PA is well defined. Then the system of linear equations PAx = b has infinitely many solutions.

C

Let A and B be two matrices such that reduced echelon form of A and B are the same. Then $\text{rank}(A)$ > $\text{rank}(B)$.

D

Let Ax = 0 be a system of linear equations such that reduced echelon form of the coefficient matrix A is the identity matrix. Then the system Ax = 0 has infinitely many solutions.