Find the rank and nullity of the matrix; then verify that...

Name: Find the rank and nullity of the matrix; then verify that the values obtained satisfy Formula (4) in the Dimension Theorem. A = [ 1 4 4 4 8; 3 -4 -4 -4 -24; -3 0 0 0 12; 4 4 4 4 -4 ] rank(A) = nullity(A) = rank(A) + nullity(A) =
Uploaded: 2023-04-08T02:17:43-08:00
Duration: 5 min 44 s
Channel: Zhumagali Shomanov
Description: Find the rank and nullity of the matrix; then verify that the values obtained satisfy Formula (4) in the Dimension Theorem. A = [ 1 4 4 4 8; 3 -4 -4 -4 -24; -3 0 0 0 12; 4 4 4 4 -4 ] rank(A) = nullity(A) = rank(A) + nullity(A) =

Find the rank and nullity of the matrix; then verify that the values obtained satisfy Formula (4) in the Dimension Theorem. A = [ 1 4 4 4 8; 3 -4 -4 -4 -24; -3 0 0 0 12; 4 4 4 4 -4 ] rank(A) = nullity(A) = rank(A) + nullity(A) =

Transcript

00:01 In this question, we are asked to determine the rank and nullity of the given matrix.

00:05 And to do that, we need to reduce it to a row echelon form.

00:09 To reduce it to a row echelon form, we need to multiply the first row by negative 3 and add it to the second row, multiply the first row by 3 and add it to the third row, and multiply the first row by negative 4 and add it to the last row.

00:38 We are doing that to get rid of the entries below 1, to get rid of these entries.

00:46 We will rewrite the first row.

00:54 In the second row, we are going to get 0.

00:58 4 times negative 3 is negative 12.

01:01 Negative 12 minus 4 is negative 16.

01:07 And it's going to be pretty much the same for all other entries, right? because they're the same.

01:12 So it's going to be negative 16 three times.

01:16 And then it's going to be 8 times negative 3 is negative 24.

01:20 And negative 24 minus 24 is negative 48.

01:24 Now let's move on to the third row.

01:29 We are going to get 0.

01:30 Then 4 times 3 is 12.