midterm_1_sample_solutions

midterm_1_sample_solutions - MA 35100 SAMPLE MIDTERM EXAM...

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

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.

Unformatted text preview: MA 35100 SAMPLE MIDTERM EXAM #1 SOLUTIONS Problem 1. Consider a linear transformation T : R 2 → R 3 which satisfies T 1 = 1 2 and T 1 = 3 1 . a. Find the matrix A of this linear transformation. b. Compute its reduced row-echelon form E = rref( A ). c. Does there exist a vector ~x ∈ R 2 such that T ( ~x ) = 12 4 3 ? Explain. Solution: (a) We use Theorem 2.1.2 on page 47 of the text. The matrix of the linear transformation is A = T ( ~e 1 ) T ( ~e 2 ) = 1 3 2 0 0 1 (b) To compute the reduced row-echelon form, we subtract 2 times the first row from the second, then divide the second row by- 6: 1 3 0 1 0 1 Now subtract 3 times the second row from the first, then subtract the second row from the third: E = 1 0 0 1 0 0 (c) For there to exist such a vector, we consider the matrix product T ( ~x ) = A~x i.e., 12 4 3 = 1 3 2 0 0 1 x 1 x 2 = x 1 + 3 x 2 2 x 1...
View Full Document

This note was uploaded on 10/18/2010 for the course MATH 351 taught by Professor Egoins during the Spring '10 term at Purdue.

Page1 / 2

midterm_1_sample_solutions - MA 35100 SAMPLE MIDTERM EXAM...

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

View Full Document
Ask a homework question - tutors are online