MATH-205 Midterm: Bates MATH 205 110907ross205exam
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Name: let a be as the matrix given on the front cover of this exam; note the rref form of [a|i4] is given there. Let b be a column vector in r4 with entries b1, b2, b3, and b4. Find a basis for col(a) using the ideas presented in class. Express the fth column vector in a as a linear combination of the basis vectors in (1b), and verify that the linear combination is correct by evaluating it; show the work. Find a basis for nul(a) using the technique presented in class. Let b be as the matrix given on the front cover of the exam. Note that b has the same columns as a, just in a di erent order. In terms of linear combinations, give a good argument why col(b) and. Col(a) must be identical. (this is a general truth ).
