Select the correct answer.

Which elementary row operation will reduce the x–element in row 2 to 0 in this matrix?

Option C. -2R1 + R2 will reduce the x element in row 2 to 0 in the given matrix.

Step-by-step explanation:

Step 1:

The values on the second row of the given matrix are 2, 1, and 0. The 2 is multiplied with x, the 1 is multiplied with y and the 0 is multiplied with z.

So the x element in the second row of the given matrix is 2.

We must find an operation such that this value becomes 0.

Step 2:

The x element in row 1 (R1); 1,

The x element in row 2 (R2); 2, and

The x element in row 3 (R3); 2.

So we substitute these values in the given operations.

Option A. 2R1 + R2 = 2(1) + 2 = 4,

Option B. 2R3 - R2 = 2(2) - 2 = 2,

Option C. -2R1 + R2 = -2(1) + 2 = 0,

Option D. R1 + R2 = 1 + 2 = 3.

Step 3:

Of the given operation, only option C attains a value of 0 while the others do not. So option C is the answer.

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