MA 2071 A '98 Final Exam Name:
Section Number: .
Show your work in the space provided. Unsupported answers may not
receive full credit.
- Use Gauss-Jordan elimination to solve the following linear
x+2y-z = 4
2x+4y+3z = 5
-x-2y+6z = -7
- Explain the following terms or statements.
- The set of vectors is linearly independent.
- The set of vectors is a basis for a vector space V.
- Rank of an matrix A.
- L is a linear transformation from to
- The matrix A is invertible.
- One of the following statements about an matrix is
not equivalent to the
others. Find the one that is not equivalent and explain why it isn't.
- A is nonsingular.
- only has the trivial solution.
- A has rank n.
- Zero is an eigenvalue of A.
- Suppose that L is the function from into
defined by L(x,y,z) = (x+y,x-y,0). First, show that
L is a linear transformation. Then compute the standard matrix
representation of L.
- Let W be the subset of P2 consisting of linear combinations
of the three polynomials . First, show that W is
a subspace, and then determine a basis for and the dimension of W.
- For the following matrix A, find a matrix P, if possible,
such that P-1 A P is a diagonal matrix. If it is not possible,
explain why not.
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