Download practice exam for math 511 linear algebra and more Quizzes Linear Algebra in PDF only on Docsity!
MATH 511, Fall 2021: Exam 1
70 minutes
September 23, 2021
Name:
Show your work and justify your answers.
Explain the thinking behind your conclusions!
The exam has 8 pages, including this cover page.
Collaboration is NOT allowed. The use of textbooks, notes, notecard, graphing/computation technol- ogy, cellphones or headphones is NOT allowed.
Any evidence that indicates use of unauthorized resources will be ground for disciplinary actions such as a zero grade and/or being reported to the WSU Office of Student Conduct and Community Standards.
SIGN PLEDGE:
I pledge my honor that I have neither given nor received aid, nor have I used unauthorized resources, on this examination.
Signed:
Problem Max
Total 65
1 13 points.
(a) Consider a 4 × 4 matrix
A =
Find both det(A) and det(kA), where k is a non-zero scalar number. Show your work.
(b) Find all values of λ for which the 2 × 2 matrix B is singular.
B =
1 − λ
√^3
3 − 1 − λ
3 15 points. Find the LU factorization of the matrix.
A =
4 18 points. In parts (a), (b), (c), and (d) of this question, the matrix A is given by:
A =
(a) Compute det(A).
(b) Find A−^1 provided it exists. If it does not exist, explain why.
5 9 points. Consider a linear system A⃗x = ⃗ 0 whose augmented matrix is of the form
2 3 β 0
(a) Is it possible for the system to be inconsistent? Explain.
(b) For what values of β will the system have infinitely many solutions? Show your work.
(c) Assume that B is another nonsingular 3 × 3 matrix such that 2⃗ b 1 − ⃗b 2 + ⃗b 3 = (1, − 3 , 0)T^ , where ⃗ b 1 , ⃗b 2 , and ⃗b 3 are columns of the matrix B. Is the linear system B⃗x = (1, − 3 , 0)T^ consistent? If so, how many solutions does it have? Briefly explain your answer.
Blank page for additional work – please label clearly if you want this page graded!
