# sol52 - Partial Solution Set Leon Section 5.2 5.2.1 For...

This preview shows pages 1–2. Sign up to view the full content.

Partial Solution Set, Leon Section 5.2 5.2.1 For each of the following matrices, determine bases for the four fundamental subspaces. (a) A = ± 3 4 6 8 ² . The row-echelon form of A is ± 3 4 0 0 ² , from which we obtain three of the four bases: (a) For N ( A ), we can use { (4 , - 3) T } . (b) For R ( A T ), we can use { (3 , 4) T } . (c) For R ( A ), we can use { (1 , 2) T } . To ﬁnd a basis for N ( A T ), we either use elimination on A T or take advantage of what we’ve learned about orthogonal subspaces by now. In either case, we obtain something very much like { (2 , - 1) T } . (c) The matrix is A = 4 - 2 1 3 2 1 3 4 . As in (a), we ﬁrst ﬁnd the row-echelon form of A , which is U = 4 - 2 0 7 / 2 0 0 0 0 . The bases: (a) For N ( A ), { 0 } . (b) For R ( A T ), we can use { (4 , - 2) T , (1 , 3) T } . (c) For R ( A ), we can use { (4 , 1 , 2 , 3) T , ( - 2 , 3 , 1 , 4) T } . After elimination on

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

sol52 - Partial Solution Set Leon Section 5.2 5.2.1 For...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online