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

1. What is a transformation (function or mapping) T from R^n to R^m

2. What is the range of T?

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

4. How are matrix entries noted?

5. What is an orthonormal set?

6. An nxn matrix with n distinct eigenvalues is ______________

7. What is an orthonormal set?

8. The vector ŷ is called the _________________________ and the vector z is called the __________________________.

9. Let {u1, ...., up} be an orthogonal basis for a subspace W of R^n. For each y in W, the weights in the linear combination y = c1u1 + c2u2+ .... + cpup are given by

10. Let A = [a b]. If ad - bc != 0, then a is _______________
[c d]
and _______ = 1/(ad-bc) [d -b]
[-c a]

11. If A is an m x n matrix, with columns a1, a2, ...., an, and if b is in R^m, the ____________________ has the same solution set as the ___________, which in turn has the same solution set as the system of linear equations whose _________________________ is _____________.

12. 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 ___________________________________.

13. What is similarity?

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

15. A transformation (or mapping) T is linear if

16. When is the volume only nonzero for a parallelpiped?

17. General solution

18. Pivot position

19. A nxn matrix with n distinct eigenvalues is _____________

20. A set {u1, .... ,up} is an orthonormal set if ________________________________

21. What is cofactor expansion of the determinant?

22. If a matrix A, has n columns, then _______________________ = n

23. When is λ an eigenvalue of a matrix?

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

25. What is the multiplicity of an eigenvalue?

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