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Linear Algebra Review (new)
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Linear Algebra Review (new)
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25 Questions

1. The columns of a matrix A are linearly independent if and only if ______________________---

2. u + 0 = 0 + u = u

3. Pivot position

4. If u = [u1, u2, .... un] and v = [v1, v2, .... vn] then the inner product of u and v is

5. In geometric terms, two vectors are linearly dependent if and only if__________________________________________

6. When is an indexed set of vectors said to be linear independent?

7. For any scalar c, the length of cv is

8. If v1, .... vp are in a vector space V, then ____________________ is a subspace of V.

9. c (du) = (cd) u

10. y = ŷ + z with z orthogonal to u if and only if α = _________________ and ŷ = ___________________

11. If T is determined by a 3 x 3 matrix, and if S is a parallelpiped in R^3, then volume of T(S) = _____________________

12. What is an eigenvalue?

13. What does the absolute value of the determinant become when a matrix is a 3 x 3 matrix?

14. When is a system of linear equations said to be homogeneous?

15. Besides linear combination of vectors, how can the matrix A be thought of?

16. What is the multiplicity of an eigenvalue?

17. If a set S ={v1, v2, ... vp} in R^n contains the zero vector then the set is ____________________________

18. If A is an m x n matrix, with columns a1, a2, ..., an, and if x is in R^n, then the product of A an dx , denoted by Ax, is what?

19. A mapping T: R^n => R^m is said to be ___________ R^m if each b in R^m is the image of AT LEAST ONE x in R^n OR when the range of T is ALL of the codomain R^m

20. Suppose L is the line through 0 and v, described by equation (4). Adding _______________ produces the translated line. Note that _____________________. We call this ____________________________. Thus the solution set of Ax=b is ___________________________________.

21. In general, when does a set of vectors [v1, v2, .... vp]in R^m span(or generates) R^m

22. What is the parametric vector form?

23. What is the inverse of an nxn matrix in terms of the adjugate?

24. Let T: R^n => R^n be a linear transformation and let A be the standard matrix for T. Then T is invertible if and only if A is an ______________________. In that case, the linear transformation S given by S(x) = A^-1x is the ______________

25. The pivot columns of a matrix A form a ___________________

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