MTH 108 Midterm: MTH 108 F00 Midterm Test 2 2005 Solutions
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2 (cid:12)(cid:12)(cid:12)(cid:12: let a and b be 4 4 matrices, where |a| = 3 and |b| = 2. = (cid:12)(cid:12)2b 1a2(cid:12)(cid:12) = |2b 1||a2| = 24|b| 1 |a|2 = 24/2 3 = 8 9 = 72 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (2b 1a2)t(cid:12)(cid:12)(cid:12) V = |(u v) w| = |(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) j i k. W| = |( 6, 3, 0) (1, 2, 3)| = | 6 6| = | 12| = 12. Mk (a) find the standard form of the equation for the plane through the points p = (2, 1, 2), Q = (1, 1, 1) and r = (1, 0, 2). Op = ( 1, 1, 1) (2, 1, 2) = 1. Plane is perpendicular to x + 2y + z = 3, so is parallel to the normal from that plane (1, 2, 1). n = (1, 2, 1) (1, 0, 0) = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) i j k.
