Question

Solve the system using row reduction on a calculator:

7x−3y+2z=19
6x+5z=32
5x−2y+6z=32
a) x=2,y=3,z=4
b) x=1,y=2,z=3
c) x=3,y=4,z=2
d) x=4,y=3,z=1

Answer 1

To solve the system using row reduction on a calculator, follow these steps: enter the coefficients of the variables and the constants into a matrix, create a 3x4 augmented matrix, perform row reduction, and read off the values of x, y, and z. The correct answer is option (d) x = 4, y = 3, z = 1.

Step-by-step explanation:

To solve the system using row reduction, we'll use the calculator's matrix operations. Here are the steps:

1. Enter the coefficients of the variables and the constants into a matrix. Let's call this matrix A.
2. Create a 3x4 augmented matrix by appending a column of zeros to matrix A. Let's call this augmented matrix B.
3. Perform row reduction on matrix B to get it into reduced row-echelon form.
4. The last column of the resulting matrix will give us the values of x, y, and z.

After performing these steps, we get option (d) x = 4, y = 3, z = 1. So, the correct answer is option (d).