1, but elimination (with 1.2. Find a matrix A for which a1,1 = a2,2 = a3,3 = no row exchanges) produces two negative pivots (the first pivot is 1).

1. Let A be a matrix with linearly independent columns. Select the best statement. A. There is no easy way to tell if such an equation has nontrivial solutions. B. The equation Ax=0 always has nontrivial solutions. C. The equation Ax=0 has nontrivial solutions precisely when it has more rows than columns. * D. The equation Ax=0 has nontrivial solutions precisely when it has more columns than rows. E. The equation Ax=0 never has nontrivial solutions. F. The equation Ax=0 has nontrivial solutions precisely when it is a square matrix. G. none of the above [4 20 8 2. Let A= 3 14 [1 9 18] We want to determine if the columns of matrix A and are linearly independent. To do that we row reduce A. To do this we add We then add times the first row to the second. times the first row to the third. We then add We conclude that times the new second row to the new third row. A. The columns of A are linearly independent. B. The columns of A are linearly dependent. C. We cannot tell if the columns of A…