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Linear Algebra Review
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Linear Algebra Review
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25 Questions

1.
This is

2.
This is

3. Why is matrix multiplication defined the way it is defined?

4.
This is

5. 1. Row space
2. Column space
3. Null space
4. Left null space

6. If λ_i is a repeated root of the characteristic polynomial, it is called a degenerate eigenvalue with algebraic multiplicity greater than 1.

7.
The set of in V such that T(x)=0

8.
The set of all output values the function may produce

9.
A matrix is said to be in row echelon form (REF) if all entries below the leading ones are zero.

10.
This is

11.
The trace of A is the sum of its eigenvalues.

12.
A symmetric matrix equals to its transpose

13.
λ_i are the eigenvalues of A

14. rank(A) + nullity(A) = n

15.
This is

16. Finds an approximate linear model by minimizing the squared error

17.
This is

18. A system of 2 equations defines 2 lines in 2D, a system of 3 equations defines 3 planes in 3D, and so on.

19.
An n-by-n matrix P is positive semidefinite if

20. What is the dimension of the column space?

21.
This is

22. the column space of the matrix M consists of all possible linear combinations of the columns of the matrix M.

23.
This is

24. To calculate the components of a vector in a generic basis, we need to solve a system of equations.
To calculate the components of a vector in an orthogonal or orthonormal basis, we just need to compute projections.

25. A vector space consists of a set of vectors and all linear combinations of these vectors.

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