MATH 3130 Midterm: Math3130PracticeExam1
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Sample exam 1 - math 3130 - intro to linear algebra. No calculators with linear algebra capabilities allowed: in each case the augmented matrix for a system of linear equations has been reduced by row operations to the given form. For each matrix answer the following: (a) is the matrix in reduced row echelon form, row echelon form, or neither, (b) is the linear system consistent or inconsistent, (c) nd the general solution, if applicable. (i) . 1 2 (cid:21) compute the following matrices, if possible, otherwise explain why it is impossible. Ab, ba, (ab)t , at b t , b 1: using the inversion algorithm, decide whether the matrix below is invertible or not. 4 1: determine the lu decomposition of the matrix. 3 (a) compute det(a) by the co-factor expansion method. (b) find all values of x such that a is not invertible. (c) use elementary row operations to reduce a to a row echelon form.
