Question 1
 
 Given that the augmented matrix 
[1 0 | -2]
[0 1 | 3]
[0 0 | 0]
determine whether the corresponding system of equations has a solution. Find the solution(s)  if there is any.
 
Answer

 Infinite solutions (-2t+3, t)

 unique solution (-2, 3)

 no solution

 infinite solutions (-2t, 3t)
10 points
Question 2
 
 Given the following augmented matrix in row-reduced form, 
[1 0 1 | 2]
[0 1 0 | -1]
determine whether the system has any solution(s). Find the solutions if there is any.
Answer

 infinite solutions (2 – t, -2 – t, 0)

 unique solution ( 2, -2, 0)

 no solution

 infinite solutions (2 – t, -1, t)
10 points
Question 3
 
 Solve the system of linear equations using the Gauss-Jordan elimination method.
2x-y=0
x+3y=7
2x+9y=20 
The solution is:
Answer

 (3t+1, t) for any t

 (3, 0)

 (1, 2)

 No solution
10 points
Question 4
 
 Solve the system of linear equations, using the Gauss-Jordan elimination method:
2x + y – z =4
6x +3y -3z = 12
Answer

 x=k, y=t, z= 2k +t – 4

x=k, y=4- 2t +k, z= t

x=k, y=t, z= 2k -t + 4

 no solution
10 points
Question 5
 Determine the value of k so that the following system of linear equations has a solution and then find the solution.
3x+4y=5
x+ 7y = 13
8x + ky = 10
Answer

 k=8, x= -7, y=2

 k=9, x= -1, y=2

 k=8, x= -2, y=1

 k=9, x= -7, y=2
10 points
Question 6
 
 Given Matrix, find the size and a23
[1 -1 0]
[4 2 -3]
Answer

 Size: 3×2, a23=-3

 Size: 3×2, a23=0

 Size: 2×3, a23=-3

 Size: 2×2, a23= 0
10 points
Question 7
 
 Perform the indicated operations.
2[1 0] – [2 -1] + [0 -1]
 [0 1]  [-1 2]  [-1 0]
Answer

[-2 0]
[-4 -2]

[0 -2]
[-2 0]

[-4 -2
[-4 0]

[0 0]
[0 0]
10 points
Question 8
 
 Find the transpose of the following matrix
[3 4]
[5 6]
[7 8]
Answer

[4 3]
[6 5]
[8 7]

[3 5 7]
[4 6 8]

[4 6 8]
[3 5 7]

[8 6 4]
[7 5 3]
10 points
Question…