Question

Determine a correct sequence of row operations to change the matrix D 1) to the matrix:

a. 3R2 - 5R2 + Ry replaces R1
b. switch R2 and R1
c. 3R1 - 3R2 + R3 replaces R3
d. -3R2 + R3 replaces R2

Answer 1

To change matrix D to the given matrix, follow these steps: multiply R2 by 3, subtract 5R2 from R1 and add R3, swap R1 and R2, multiply R1 by 3, subtract 3R2 from R1 and add R3, and subtract 3R2 from R3.

Step-by-step explanation:

To change matrix D to the given matrix, we need to perform the following row operations:

a. Multiply the second row (R2) by 3, subtract 5 times the second row from the first row (R1), and add the third row (R3) to the first row.
R1 = 3R2 - 5R2 + R3

b. Swap the first row (R1) and the second row (R2).
Switch R2 and R1

c. Multiply the first row (R1) by 3, subtract 3 times the second row from the first row (R1), and add the third row (R3) to the first row.
R3 = 3R1 - 3R2 + R3

d. Subtract 3 times the second row from the third row (R3).
R2 = -3R2 + R3