Math 2568 m2568au17mt2_sample

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Published on 31 Jan 2019
School
Ohio State University
Department
Mathematics
Course
MATH 2568
Professor
Math 2586 sample midterm 2
Hsian-Hua Tseng
October 2017
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Problems
1. Give the detailed definition of vector spaces.
2. Consider the following matrix:
A=
12 1
23 5
107
.
Find bases for the following subspaces:
(a) N(A), the null space of A.
(b) R(A), the range of A.
3. Consider the following vectors in R3:
v1= (3,5,0), v2= (6,4,2).
Find a vector uR3such that
(a) The length of uis 1.
(b) uis orthogonal to both v1and v2.
4. Determine whether the following matrix is invertible or not:
A=
12 11
1 3 15
01 5
.
If Ais invertible, compute A1.
5. Determine the dimension of the row space of the following matrix:
A=
123
4 5 6
98 7
10 11 12
.
1
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Document Summary

Problems: give the detailed de nition of vector spaces, consider the following matrix: Find bases for the following subspaces: (a) n (a), the null space of a. (b) r(a), the range of a: consider the following vectors in r3: v1 = (3, 5, 0), v2 = (6, 4, 2). Find a vector u r3 such that (a) the length of u is 1. (b) u is orthogonal to both v1 and v2: determine whether the following matrix is invertible or not: 5: determine the dimension of the row space of the following matrix: