Linear Algebra Revision Quiz Form
Test your linear algebra knowledge with this revision quiz. Please answer all questions to the best of your ability.
What is the dimension of the vector space ℝ³?
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Given the matrix A = [[1, 2], [3, 4]], calculate its determinant.
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Which of the following sets of vectors in ℝ² is linearly independent?
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[(1, 0), (0, 1)]
[(1, 2), (2, 4)]
[(0, 0), (1, 1)]
Find the eigenvalues of the matrix [[2, 0], [0, 3]].
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If a system of linear equations has more variables than equations, what can you say about its solutions?
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It has no solution
It has a unique solution
It may have infinitely many solutions
Write the general form of a 2x2 identity matrix.
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What is the rank of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
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Given vectors u = (2, -1) and v = (1, 3), compute their dot product.
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What does it mean for a matrix to be invertible?
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Which property must a set satisfy to be a subspace of a vector space?
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Closed under addition and scalar multiplication
Contains only the zero vector
Has at least two vectors
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