Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Let: What is the rank of A? What is the matrix norm of A? What are the distances

ID: 2902922 • Letter: L

Question

Let:

What is the rank of A? What is the matrix norm of A? What are the distances from A to the rank 1, rank 2, and rank 3 matrices? Here we always use the matrix norm which corresponds to the Euclidean vector norm.

I have the MATLAB Answers:

rank(A) = 4

norm(A) = 2.4752

I NEED HELP DOING THE HAND COMPUTATIONS - THANK YOU!

Let: What is the rank of A? What is the matrix norm of A? What are the distances from A to the rank 1, rank 2, and rank 3 matrices? Here we always use the matrix norm which corresponds to the Euclidean vector norm. I have the MATLAB Answers: rank(A) = 4 norm(A) = 2.4752 I NEED HELP DOING THE HAND COMPUTATIONS - THANK YOU!

Explanation / Answer

Your matrix

Subtract the 1st row from the 2nd row

Multiply the 1st row by -1

Subtract the 1st row from the 3rd row

Subtract the 1st row from the 5th row

Multiply the 1st row by -1

Subtract the 1st row from the 6th row

Divide the 2nd row by -2

Subtract the 2nd row from the 3rd row

Multiply the 2nd row by -1

Subtract the 2nd row from the 4th row and restore it

Multiply the 2nd row by 2

Subtract the 2nd row from the 5th row and restore it

Multiply the 2nd row by -1

Subtract the 2nd row from the 6th row and restore it

Restore the 2nd row to the original view

Subtract the 3rd row from the 5th row and restore it

Multiply the 3rd row by -2

Subtract the 3rd row from the 6th row and restore it

Divide the 4th row by 3/2

Multiply the 4th row by -1/2

Subtract the 4th row from the 5th row and restore it

Multiply the 4th row by 7/2

Subtract the 4th row from the 6th row and restore it

Restore the 4th row to the original view

Calculate the number of linearly independent rows

Matrix rank is 4

? A1 A2 A3 A4 1 1 1 1 1 2 1 -1 1 0 3 -1 0 0 1 4 0 -1 0 1 5 -1 1 0 1 6 1 0 -1 1