MATH 336 Final: MATH 336 NIU Final092

• School: NIU
• Department: Mathematics
• Course: MATH 336
• Professor: All

Document Summary

No calculators: (10 pts) (a) if ad bc 6= 0, then we know that the matrix (cid:20) a b d (cid:21) has an inverse of the form c. 1 ad bc (cid:20) w x z (cid:21). y. If ad bc 6= 0, then (cid:20) a b c d (cid:21) 1. 1 ad bc (cid:20) d b a (cid:21), so w = d, x = b, y = c, and z = a. C (b) use the formula in part (a) to nd the inverse of the matrix (cid:20) (cid:20) cos . Sin sin cos (cid:21) 1. 1 cos2 + sin2 (cid:20) cos sin cos (cid:21) 1 sin sin cos . Sin cos (cid:21), where is a real number. = (cid:20) cos sin cos (cid:21) sin : (20 pts) use gauss-jordan reduction to solve the following linear system. X1 2x2 +x3 x4 = 4 x1 +2x2 +x3 +4x4 = 3.