MATH 3000 Quiz: MATH 331 Mizzou Quiz 5 Solutions

• School: Mizzou
• Department: Mathematics
• Course: MATH 3000
• Professor: All

Document Summary

1). (5 points) for the matrix a = (cid:20) 9. 3 (cid:21) either nd the inverse, or determine that no inverse exists, by using the algorithm that starts with [ a | i2 ]. (cid:20) 9. 9 (cid:21) so a 1 = (cid:20) 3 26. 2). (5 points) let b be a 4 4 matrix. Suppose that you know that 5b1 2b3 + b4 = 0. Recall that the bj are the columns of b. The given equation means that [ 5 is a (nonzero) solution to bx = 0. By theorem 1. 4. 3, this means that b is singular (i don"t expect you to know the theorem number). Equivalently, b does not reduce to i4 so there will be 4 variables and at most 3 leading 1"s. This will give at least one free variable. Thus there are in nitely many solutions to bx = 0.