Given the following system of equations, type the coefficient matrix.

Question

5x −  y = 6

2x + 7y = 9

Answer 1

Hi, Kellyn!

The key to this problem is to note that a coefficient matrix is formed by inputting the coefficients of each of the variables in the system of equations.

Let's label 5x - y = 6 as Equation A. In this equation, both x and y have a coefficient, which we will label A_x and A_y. The values of these coefficients are A_x = 5 and A_y = -1.

We can analyze 2x + 7y = 9 (Equation B) in the same way, which would give us B_x = 2 and B_y = 7.

We can then assemble our coefficient matrix, which takes the form of a 2x2 matrix with the A coefficients in the top row and the B coefficients in the bottom row.

( Ax Ay

Bx By ) (the parentheses should be large and encompass all of the values)

We can then plug in our values to obtain the following matrix:

( 5 -1

2 7 )

I hope that this explanation is helpful, and please don't hesitate to reach out if you have any further questions!