linear help

4 0 2 . (2 points) Consider the linear system Ax : b where A : f0 2f and b : fol . Show that 11 1J 1111 the linear system AX = b is inconsistent. Find a least squares solution )2 of AX = b. Is the least squares solution you found unique? Explain. If not, nd a diiferent least squares solution. 1 0 1 0 1 1 . Show that the linear I0 1 1 I [1 0 lj [OJ system Ax : b is inconsistent. Find a least squares solution :2 of Ax : b. Is the least squares and vector b = 2 0 . (2 points) Consider the matrix A = 2 I solution you found unique? Explain. If not, nd a different least squares solution. 1 2 . (2 points) Consider the matrix A = ll of and let 12 1J f : Ax - Ax (1) Verify by direct calculation that Vf = 2ATAX. . (2 points) Consider the function of n variables given by f(X) = ||3Xa||2 (2) Where a is a constant vector in R". Calculate V f using the strategy illustrated in example 4 from lecture 15. Show all work. . (2 points) Does the linear system [10 0] [1] Hi: J3! 3 I13 9|x'l3l \" I1416| |8| [1525J [12] have a unique least squares solution? Explain