Practice Sparse Matrices (21.15.3) - Linear Algebra - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Define a sparse matrix.
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Think about the ratio of non-zero to zero elements.
Question 2.
What is one application of sparse matrices?
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Consider engineering simulations.
3Question 3.
What defines a sparse matrix?
- A matrix with all non-zero elements
- A matrix with a high ratio of zero elements
- A matrix that can be only square
- A matrix whose dimensions are equal
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Consider the balance between zero and non-zero values.
4Question 4.
True or False: All matrices are sparse matrices.
- True
- False
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Reflect on the definition we discussed.
Question 5.
You have a large matrix from finite element analysis with only 12 non-zero values out of 100 elements. How would you convert this to a sparse matrix representation?
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Think about what it means to store only what's necessary.
Question 6.
Analyze a scenario where using a dense matrix for a problem caused inefficiencies. How would sparse matrices solve these pitfalls?
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Consider the difference between filling a balloon and only keeping the essential air!

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