National University
of Computer and Emerging Sciences
Chiniot-Faisalabad Campus
MT104 – Linear Algebra
Assignment No. 1
Title: Linear Combinations and Span
Spring 2021
Maximum Marks: 40 Due Date: 29th March 2021
Submitted By
Name: _________________________
Student ID: _________________________
Section: _________________________
Submitted To
Amjad Hussain
Assistant Professor Mathematics
Details of Obtained Marks
Question Number 1 2 3 4
Total
CLO Number 1 1 1 1
Total Marks 10 10 10 10 40
Obtained Marks
MT104 – Linear Algebra
Assignment No. 1
Title: Linear Combinations and Span
No. Course Learning Outcome (CLO) Statements Taxonomy Level PLO
01 Find Linear combinations and span of vectors. C2 1
Consider the vectors,
0 1 −3 −1
𝑢 = [ 2 ] , 𝑣 = [−1 ] , 𝑤 = [ 4 ], and 𝑦 = [ 0 ]
4 1 −1 −3
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Question # 1
Can 𝒚 be written as a linear combination of 𝒖, 𝒗, and 𝒘? If yes, find that combination.
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Question # 2
Can 𝒘 be written as a linear combination of 𝒖, 𝒗? If yes, find that combination.
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Question # 3
Are 𝒖, 𝒗, w and 𝒚 co-planer? Prove or disprove by using the definition of linear
combinations.
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Question # 4
Find the value of
a. 𝒔𝒑𝒂𝒏 {𝒖, 𝒗, 𝒘, 𝒚}.
b.𝒔𝒑𝒂𝒏 {𝒖, 𝒗, 𝒘}.
Is 𝒔𝒑𝒂𝒏 {𝒖, 𝒗, 𝒘} = 𝒔𝒑𝒂𝒏 {𝒖, 𝒗, 𝒘, 𝒚}? prove or disprove with complete mathematical
solution.
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