MATH 3130 Midterm: Math3130PracticeExam2
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Practice for exam 2 - math 3130 intro to linear algebra. Given the matrix (1) compute det(a) by the co-factor expansion method. (2) find all values of x such that a is not invertible. (3) use elementary row operations to reduce a to a row echelon form. 2 0 4 decide whether a is invertible or not. Solve the following linear system using cramer"s rule: x + y + z = 0 x 2y + 2z = 4 x + 2y z = 2. Exercise 4 (a) find the complete solution of the linear system ax = b, where. Consider the matrix below (which happens to be the transpose of the matrix a in exercise 2(a). ) Write down a basis for the column space of b. (c) express the free column(s) of b as a linear combination of the columns listed in the basis found in (b). Determine whether the following four vectors span r3 or not.
