[suman]

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Can you provide me the Assignment for MTH 102: Linear Algebra of Department of Mathematics and Statistics Indian Institute of Technology – Kanpur?

[Vishal Kotkar]

The Assignment for MTH 102: Linear Algebra of Department of Mathematics and Statistics Indian Institute of Technology – Kanpur is as follows:

Problem Set 1

Problems marked (T) are for discussions in Tutorial sessions.

1. (T) If A is an m × n matrix, B is an n × p matrix and D is a p × s matrix, then show that A(BD) = (AB)D (Associativity holds).

2. If A is an m × n matrix, B and C are n × p matrices and D is a p × s matrix, then show that
(a) A(B + C) = AB + AC (Distributive law holds).
(b) (B + C)D = BD + CD (Distributive law holds).

3. (T) Let A and B be 2 × 2 real matrices such that A x/y = B x/y for all (x, y) ∈ Rn
Prove that A = B.

4. Let A and B be m × n real matrices such that Ax = Bx for all x ∈ Rn. Then, A = B

5. For two matrices A and B show that
(a) (A + B)T = AT + BT if A + B is defined.
(b) (AB)T = BTAT if AB is defined.

Assignment for MTH 102: Linear Algebra IIT Kanpur