1. Consider the following system of linear equations: T1 + kr2 = 2 kri + x2 + 13 =1 X1+ x2 + x3 =k For which values of k will the system have: infinitely many solutions? no solution? one unique solution? 2. Find all the solutions to the system below describing your solution set in vector notation using free variables. T1 - 3x2 + 2x3+ 2x4 + 2x5 = 1 -x1 + 3x2 + 4x4 - 6x5 1 2x1 - 6x2 + 3x3 + 6x4 + x5 = 1 : and B= 3. Given the matrices A = show that A and B have the same eigenvalues. 47 1 8 4. Let A = 1 2x 2x x (a) Find the determinant of A. (b) For what values of x is the matrix A nonsingular?

The top 2 are wrong

A student in an Chemistry class has test scores of 70, 63, 61, and 68. The final exam is worth the same amount as 3 test grades.    How would you find the lowest grade that could be earned on the final exam that would still result in at least a B in the course (average score of 80%?)

what is 3 less than 8times a number