Massachusetts institute of technology
18.06-Linear Algebra
Matrix theory-Problem Set with Solutions
PARTA: BASIC PROBLEMS
Problem 1: Matrix Addition
Given:
A=[2 −1
3 4 ], B=[1 5
−2 6]
Find A+B.
Solution:
A+B = [2+1 −1+ 5
3+(−2) 4+6 ], = [3 4
110]
Problem 2: Scalar Multiplication
If
A=[4 −2
1 3 ]
Find 3A
Solution:
3A=[12 −6
3 9 ]
PART B: MATRIX MULTIPLICATION
Problem 3: Product of Matrices
A=[1 2
3 4], B=[2 0
1 5],
Find AB.
Solution:
AB=[(1)(2)+(2)(1) (1)(0)+(2)(5)
(3)(2)+(4)(1) (3)(0)+(4)(5)] = [410
10 20]
