MATH136 Study Guide - Midterm Guide: Elementary Matrix, Row Echelon Form, Augmented Matrix
14 May 2018
School
Department
Course
Professor
Math 136 Sample Midterm 1
1. Short Answer Problems
a) List the 3 elementary row operations.
b) Does the spanning set Span
1
2
1
,
0
1
0
,
1
0
1
represent a line
or a plane in R3? Give a vector equation which describes it.
c) State the definition of the rank of a matrix.
d) Explain why ~a ×(~
b×~c) must be a vector in the plane with vector equation
~x =s~
b+t~c,s, t ∈R.
2. Consider the system of linear equations:
x1+ 2x2−x3= 0
−x1−x2+ 3x3= 1
2x1+ 6x2+ 2x3= 2
a) What is the augmented matrix of the system?
b) Row reduce the augmented matrix of the system into reduced row echelon form, stating
the elementary row operations used.
c) Find the solution set of the system.
3. Let S=
1
2
1
,
−1
3
2
,
2
4
−1
.
a) Determine if
1
1
1
is in Span S. If so, write it as a linear combination of the vectors in S.
b) Determine if Sis linearly independent or dependent.
4. Let ~x =
1
−2
1
,~y =
1
0
−1
, and ~z =
2
3
−1
. Determine the following.
a) 2~x −3~y
b) A non-zero vector that is orthogonal to ~y and ~z.
1
34
MATH136 Full Course Notes
Verified Note
34 documents
Document Summary
Sample midterm 1: short answer problems, list the 3 elementary row operations, does the spanning set span . Give a vector equation which describes it. represent a line: state the de nition of the rank of a matrix, explain why ~a (~b ~c) must be a vector in the plane with vector equation. ~x = s~b + t~c, s, t r: consider the system of linear equations: x1 + 2x2 x3. 1: let s = , determine if . Is in span s. if so, write it as a linear combination of the vectors in s: determine if s is linearly independent or dependent, let ~x = . Determine the following: 2~x 3~y, a non-zero vector that is orthogonal to ~y and ~z. 1: consider the plane p in r3 with vector equation ~x = s . 1 s, t r: find a scalar equation for p , find the projection of ~u = .
