Practice Conditions (21.4.2) - Linear Algebra - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Define what it means for a matrix to be non-singular.
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Think about how the determinant relates to the matrix's invertibility.
Question 2.
What is the relationship between a matrix and its inverse?
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Consider what happens when you multiply the inverse with the original matrix.
3Question 3.
What must be true for a matrix to have an inverse?
- It must be singular
- It must have a determinant of zero
- It must be non-singular
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Recall the definition of singular matrices.
4Question 4.
True or False: A singular matrix cannot have an inverse.
- True
- False
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Think about how determinants affect inversibility.
Question 5.
Determine if the following matrix is invertible: A = [[4, 2], [2, 1]]. Justify your answer with calculations.
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Calculate the determinant!
Question 6.
If B = [[1, 3], [3, 7]], what can you say about its inverse and detail how you would find it?
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Recall how to calculate the determinant and apply the inverse formula.

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