MATH 240 Midterm: MATH 240 NIU Exam1 sample2

• School: NIU
• Department: Mathematics
• Course: MATH 240
• Professor: All

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No calculators: (10 pts) (a) if ad bc 6= 0, then we know that the matrix (cid:20) a b c d (cid:21) has an inverse of the z (cid:21). What are the values for w, x, y, and z? (you don"t need to show ad bc (cid:20) w x form. 1 y any work for this answer. ) (b) use the formula in part (a) to nd the inverse of the matrix (cid:20) Sin cos (cid:21), where sin : (20 pts) use gauss-jordan reduction to solve the following linear system. X1 2x2 +x3 x4 = 4 x1 +2x2 +x3 +4x4 = 3. 2x1 +4x2 +2x3 +7x4 = 5: (15 pts) find the inverse of the matrix a = numbers. (i suggest using the row reduction method. ) Check each of the four laws 5, 6, 7, and 8 for scalar multiplication. If the law is valid, give a proof.