Linear Algebra Homework # 1
YOUR NAME:
Instructions: You can either print out the homework and write your answer on it(recommended),
or other ways that clearly shows your work and computations. Write your UNI in the right top
corner of each page. and your name in the left top corner. For computational excercise, circle the
final answer. This homework is due at 4:00pm June, 1st.
Problem 1.

1
(1)  2
1
(2)
Compute the

3 5
1
4 1  1
1 0
0
2 3
1 2
1
5
following matrix multiplication.

2 1
1 0 
2 2
1
Linear Algebra Homework # 1
(3)
1 2 3
1 1 2
Your UNI:


1 2
 1 1 
1 0



1 1 2
1 3 2
(4)  2 1 0   2 5 1 
0 0 1
0 4 1
2
YOUR 
NAME:


2 2 1
7 2
(5)  1 5 2   4 1 
0 3 7
6 8
Your UNI:
Problem 2. In the following matrices multiplications, which expression make sense and which is
not? Find out each size of the matrix and compute them if they make sense.
 
1
2 5  
3
Example 1.
1 3
2
Answer: 2 × 2 matrix multiply 3 × 1 matrix, 2 6= 3, doesn’t make sense.
2 5
3
Example 2.
1 3
2
Answer: 2 × 2 matrix multiply 2 × 1 matrix, 2 = 2, this make sense. And final result would be 2 × 1
matrix..(and follow your computation)
4
(1) 1 2 3
5



3
1 2
(2)  7   1 3 
6
5 2
3
Linear Algebra Homework # 1
Your UNI:

 
3 2 5
3
(3)  4 1 3   5 
2 1 6
4



3
3 2 5
(4)  5   4 1 3 
4
2 1 6
(5)
1 3
1 2 1
5 3 1
4
YOUR NAME:
(6)
(7)
1 2 1
5 3 1
Your UNI:
1 5 1
7 9 10
1 3


1 5
 7 2 
8 11


1 5
1 5 1


7 2
(8)
7 9 10
8 11
5
Linear Algebra Homework # 1
Problem 3. A is a matrix over R, and suppose we know that
 
1
0


A 2
=
1
3
Your UNI:
and


1
2


A 1
=
1
1
(1) What is the size of A?
(2) Can you predict what is the value of the following expression?
 
2
A 4 
6
(Hint: scalar multiplication)
(3) Can you predict what is the value of the following expression?
 
1
A 3 
5
(Hint: Distributive property for matrix multiplication)


 
a
a
4
(4) Can you find the value of a,b,c such tht the 3×1 matrix  b  saitisfies A  b  =
?
4
c
c
6
YOUR NAME:
Your UNI:
7