The GATE Grind

GATE 2024 ES – Question 25

Mathematics Foundation · Linear Algebra · 1 mark · Multiple select

For a vector X, linear operators A, B and scalar λ,which identities hold?

  1. $(A+B)X=AX+BX$
  2. $(\lambda A)X=\lambda(AX)$
  3. $(AB)X=A(BX)$
  4. $(A+B)X=A^TX+B^TX$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $(A+B)X=AX+BX$; (B) $(\lambda A)X=\lambda(AX)$; (C) $(AB)X=A(BX)$

Explanation

Operator addition and scalar multiplication are defined pointwise, and operator composition AB applies B then A. Therefore A, B and C hold when domains are compatible. Transposition changes operators in general, so D need not hold. Select **A, B, C**.

More Linear Algebra questions

All Linear Algebra questions →