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1. Solve the homogeneous system of linear equations corresponding to the coecient matrix   −6 4 −3 4 2 2 −6 −2 −3   2. a) Solve the system having augmented matrix [A|b] below using Gaussian elimination with backward substitution. b) Find det(A). [A|b] =   1 −1 0 −1 0 0 0 1 −1 0 −1 0 6 0 0 2 0 6 0 7 0 −2 4 0 0 0 5 0 −4 0   3. a) Use Kircho's laws of electrical circuits, write a system of 5 linear equations in 5 unknowns (current ows I1 − I5) for the circuit below with resistances R1 − R8 given as 2, 3, 3, 2, 4, 2, 4 and 5 ohms, respectively, when a potential of V = 6 volts are applied. (b) Give the solution 4. Find the least squares regression line for the points (7, 2),(8, 3),(9, 2), and(10, 2), including error analysis. 5. (a) Find the determinant of the matrix A below. (b) Find | − 3A|, |AT |, |A−1 |, and |A−4 |. A =   3 0 2 0 0 1 −2 −3 0   1

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