MATH 251 Midterm: MATH 304 TAMU Homework Midterm2Preparation Solution
Document Summary
Math 304 linear algebra sections 505 and 506. Review homework for midterm exam 2 solution. Find a basis of the columns space col(a) and for the nullspace n(a). The basis of the column space is given by the columns of a, which correspond to the lead variables of the reduced row echelon form u of a. Thus, we have a basis for col(a) given by. Thus, n1 and n2 span n(a) and it follows from the entries in their 3rd and 5th row that they have to be linearly independent. Thus, n1 and n2 are a basis for n(a). If the answer is no , then extend or pare down the set to a basis of r3. , v4 cannot be basis for r3 since the dimension of r3 is 3 < 4, i. e. every basis of r3 needs to have exactly 3 elements. We have learned that every set of 3 linear independent vectors is a basis for r3.
