# 2006wtt-a23 - University of Toronto at Scarborough...

This preview shows pages 1–3. Sign up to view the full content.

University of Toronto at Scarborough Midterm Test MATA23H3 Linear Algebra I Examiner: N. Cheredeko Date: February 10, 2006 Duration: 110 minutes 1. [10 points] (a) Determine whether - 1 3 2 is a linear combination of 2 0 1 and 0 2 4 . (b) Do 2 0 1 and 0 2 4 span R 3 ? Justify your answer. 2. [10 points] (a) Find the projection of w = 1 1 1 on the normal to the plane π with equation x - 7 y + 4 z = 0. (b) Find the distance from the point P (1 , 1 . 1) to the plane π . 3. [15 points] Let u = 3 4 0 and v = 0 0 3 . (a) Find the angle between u and v . (b) State and verify the Cauchy-Schwartz inequality for u and v . (c) Find a unit vector that is perpendicular to both u and v .

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

View Full Document
MATA23H page 2 4. [15points] (a) Suppose A and B are invertible matrices and X is a matrix such that AXB = A + B . What is
This is the end of the preview. Sign up to access the rest of the document.

## 2006wtt-a23 - University of Toronto at Scarborough...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online