Determine whether the products is defined or undefined. if defined, give the dimensions of the product matrix

The product of the given matrices can be defined and will be of the order   2 × 1. So the answer is option 2.

Explanation:

In order to multiply two matrices, the matrix must have the same number of columns as the rows in the matrix. So to see if the given matrices can be multiplied we need to determine the order of both matrices.The matrix has 2 rows and 3 columns. So the order of the matrix is 2 × 3.The matrix has 3 rows with 1 column. So its order is 3 × 1.The matrix has 3 columns and the matrix has an equal number of rows, so they can be multiplied.The order of the new matrix will be the matrix's number of rows × the matrix's number of columns = 2 × 1.

defined 2*1

Step-by-step explanation:

Solve for z:
5 (z + 6) - 2 = 9 z

5 (z + 6) = 5 z + 30:
5 z + 30 - 2 = 9 z

Add like terms. 30 - 2 = 28:
5 z + 28 = 9 z

Subtract 9 z from both sides:
(5 z - 9 z) + 28 = 9 z - 9 z

5 z - 9 z = -4 z:
-4 z + 28 = 9 z - 9 z

9 z - 9 z = 0:
28 - 4 z = 0

Subtract 28 from both sides:
(28 - 28) - 4 z = -28

28 - 28 = 0:
-4 z = -28

Divide both sides of -4 z = -28 by -4:
(-4 z)/(-4) = (-28)/(-4)

(-4)/(-4) = 1:
z = (-28)/(-4)

The gcd of 28 and -4 is 4, so (-28)/(-4) = (-(4×7))/(4 (-1)) = 4/4×(-7)/(-1) = (-7)/(-1):
z = (-7)/(-1)

(-7)/(-1) = (-1)/(-1)×7 = 7:
  z = 7