please someone actually help me

Question

Question 1: Does matrix A have an inverse? Explain.

A.) No because the A2,1 and A2,2 entries are equal.

B.) Yes because the determinant of A is not 0.

C.) No because the A2,1 entry is 0.

D.) No because the determinant of A is 0.

Question 2: Identify the augmented matrix for the system of equations.

3x − 2y + 5z = 30

5x + 4z = 35

3y − 2z = −4

A.)

B.)

C.)

D.)

Question 3: Identify the augmented matrix for the system of equations and the solution using row operations.

6x + 5y = 37

4x − 3y = 12

A.)

B.)

C.)

D.)



Please give and only give the explanation and the solution.

Answer 1

d) No because the determinant is zero

[note that the matrix cannot be reduced to

row echelon form; there is a row with ALL ZER0S]

3 -2 5 30

5 0 4 35

0 3 -2 -4

6 5 37

4 -3 12

solution:

3( 6x + 5y = 37)

5( 4x - 3y = 12)

18x + 15y = 111

20x - 15y = 60

38x = 171

x=4.5

so option A