7. Systems of Equations & Matrices

Let A = and B = . Find each of the following. See Examples 2 –4. (3/2)B

Find each product, if possible. See Examples 5–7. <4x2 Matrix>

Find the values of the variables for which each statement is true, if possible. [2x2 matrix] = [2x2 matrix]

Solve by eliminating variables:

Solve each system in Exercises 25–26. (x+3)/2 − (y−1)/2 + (z+2)/4 = 3/2, (x−5)/2 + (y+1)/3 − z/4 = − 25/6, (x−3)/4 − (y+1)/2 + (z−3)/2= − 5/2

Solve each system in Exercises 25–26. (x+2)/6 − (y+4)/3 + z/2 = 0, (x+1)/2 + (y−1)/2 − z/4 = 9/2, (x−5)/4 + (y+1)/3 + (z−2)/2 = 19/4

Exercises 57–59 will help you prepare for the material covered in the next section. Solve: A + B = 3, 2A - 2B + C = 17, 4A - 2C =14

In Exercises 19–22, find the quadratic function y = ax^2+bx+c whose graph passes through the given points. (−1,−4), (1,−2), (2, 5)

In Exercises 19–22, find the quadratic function y = ax^2+bx+c whose graph passes through the given points. (−1, 6), (1, 4), (2, 9)

Solve each system in Exercises 5–18. 3(2x+y)+5z=−1, 2(x−3y+4z)=−9, 4(1+x)=−3(z−3y)

Solve each system in Exercises 5–18. x+y=−4, y−z=1, 2x+y+3z=−21

Solve each system in Exercises 5–18. 2x+y=2, x+y−z=4, 3x+2y+z=0

Solve each system in Exercises 5–18. 2x−4y+3z=17, x+2y−z=0, 4x−y−z=6

Solve each system in Exercises 5–18. 3x+2y−3z=−2, 2x−5y+2z=−2, 4x−3y+4z= 10

Solve each system in Exercises 5–18. 4x−0y+2z=11, x+2y−z=−1, 2x+2y−3z=−1