{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# exam7 - M340L Third Midterm Exam April 7 2003 1 The...

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

M340L Third Midterm Exam, April 7, 2003 1. The following two 4 × 4 matrices are row-equivalent: A = 1 1 2 1 1 3 8 0 2 4 10 1 3 5 12 0 ; B = 1 0 - 1 0 0 1 3 0 0 0 0 1 0 0 0 0 a) What is the rank of A ? b) Find a basis for the column space of A . c) Find a basis for the null space of A . d) Find a basis for the row space of A . 2. Let V =Span { 1 1 1 1 , 1 2 3 4 , 1 3 5 8 , 4 3 2 1 } ⊂ R 4 . a) What is the dimension of V ? b) Find a basis for V . c) Let W be the subspace of P 3 [ t ] spanned by the polynomials 1+ t + t 2 + t 3 , 1 + 2 t + 3 t 2 + 4 t 3 , 1 + 3 t + 5 t 2 + 8 t 3 and 4 + 3 t + 2 t 2 + t 3 . What is the dimension of W ? Find a basis for W . 3. Consider the following basis for R 3 : B = 1 2 2 , 3 7 7 , 6 12 13 a) Find the change-of-basis matrix P EB that converts from coordinates in the B basis to coordinates in the standard ( E ) basis.

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 ]}