Will anyone help me with PIVOTING a MATRIX?

Question

Pivot the system about the element in row 2, column 2. Do not completely reduce the matrix. [Recall that pivoting about an entry means to make that entry a 1 and all other entries in that column zeros.]

1 -9 -5 | -4

[ 0 -2 -4 | 7 ]

0 -9 1 | -9

i would appreciate your time, i have been stuck trying to comprehend this for hours. so far the only right answers i have are as shown below, where "_" are the numbers I cannot reach yet.

1 0 _ | _

[ 0 1 _ | _ ]

0 0 _ | _

Thank you!

Answer 1

Hi there!

For this problem, it looks like we'll want to perform some row reducing, but only in relation to that one entry so as to make every other entry in that column 0. The first step, as it looks like you've already done, is to multiply the second row by -1/2:

1 -9 -5 | -4 1 -9 -5 | -4

0 -2 - 4 | 7 → 0 1 2 | -7/2

0 -9 1 | -9 0 -9 1 | -9

From here, we'll then want to perform row operations on rows 1 and 3 to make their second entries 0:

R₁ + 9R₂

R₃ + 9R₂

So we calculate:

1 -9 -5 | -4 1 0 13 | -71/2

0 1 2 | -7/2 → 0 1 2 | -7/2

0 -9 1 | -9 0 0 19 | -81/2

And there you have your missing values. I hope this helped, and please let me know if you're still confused!

*sorry if the matrices are poorly formatted, they're way harder to write than I first thought.