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mth102 iitk |
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Re: mth102 iitk
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 |
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