Question

Which matrix represents the system of equations shown below?

y = 10
4x-5y = 3
OA 190
Α.
4-5
OB.
O C.
OD.
0 1 3
4 -5 10
6
0
-53
5 10
1 3

Answer 1

C

Explanation:

To represent the system of equations step by step using matrices, we'll start by setting up the coefficient matrix and the constant matrix. Let's go through the process:

Step 1: Write down the equations:

Equation 1: y = 10

Equation 2: 4x - 5y = 3

Step 2: Set up the coefficient matrix (matrix A):

Coefficients of Equation 2: 4 and -5

Coefficients of Equation 1: 0 and 1

A =

| 4 -5 |

| 0 1 |

Step 3: Set up the constant matrix (matrix B):

Constants of Equation 2: 3

Constants of Equation 1: 10

B =

| 3 |

| 10 |

Step 4: Combine the coefficient matrix and constant matrix into an augmented matrix (matrix [A|B]):

[A|B] =

| 4 -5 3 |

| 0 1 10 |

This augmented matrix represents the system of equations:

4x - 5y = 3

0x + 1y = 10

Each row in the augmented matrix corresponds to an equation in the system. The first column represents the coefficients of x, the second column represents the coefficients of y, and the last column represents the constants.

Therefore, the matrix that represents the system of equations is:

C.

0 1 3

4 -5 10