MATH-0070 Midterm: MATH70 exam1 Exam1-S18
Math 70 TUFTS UNIVERSITY Feb 26, 2018
Linear Algebra Department of Mathematics Sections 2,3,4
Exam 1
Instructions: No notes or books are allowed. All calculators, cell phones, or other electronic devices
must be turned off and put away during the exam. Unless otherwise stated, you must show all work
to receive full credit. You are required to sign your exam. With your signature you are pledging that you have
neither given nor received assistance on the exam. Students found violating this pledge will receive an F in the
course.
Problem Point Value Points
1 20
2 10
3 10
4 8
5 10
6 14
7 12
8 8
9 8
100
1
1. (20 points) Consider the following system of equations:
x1−2x2+ 2x3+ 10x4= 3
x1−2x2+ 5x3+ 25x4= 9
(a) Write the system as a a vector equation.
(b) Write the system as a matrix equation Ax=b.
(c) Solve the system and write your solution in parametric vector form.
2
2. (10 pts) True/false questions. For each of the statements below, decide whether it is true or
false. Indicate your answer by shading the corresponding box. There will be no partial credit.
(a) The map T:Rn→Rmdefined by T(v) = 0Rmfor all vin Rnis linear. T F
(b) Let Abe an m×nmatrix.
The range of the map x7→ Axis the span of the columns of A. T F
(c) Every set of four vectors in R3is linearly dependent. T F
(d) Every linear transformation from R3to R2is onto. T F
(e) If a set of vectors {v1,v2,v3}is linearly dependent, then one of the vectors
is a scalar multiple of one of the others. T F
Document Summary
All calculators, cell phones, or other electronic devices must be turned o and put away during the exam. Unless otherwise stated, you must show all work to receive full credit. With your signature you are pledging that you have neither given nor received assistance on the exam. Students found violating this pledge will receive an f in the course. 100: (20 points) consider the following system of equations: x1 2x2 + 2x3 + 10x4 = 3 x1 2x2 + 5x3 + 25x4 = 9 (a) write the system as a a vector equation. 1 (b) write the system as a matrix equation ax = b. (c) solve the system and write your solution in parametric vector form: (10 pts) true/false questions. For each of the statements below, decide whether it is true or false. Indicate your answer by shading the corresponding box.
