monkey3842

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Linear Algebra Help I need help figuring out these 2 problems. The answers are underneath the problem 1. T : R^2 --> R^2 , Linear Trans. T(x,y) = (x+2y, y-x) Find Ker(T). Ans: {0,0} 2. T(vector x) = Ax Linear Trans. A=[4 1] ....[0 0] (supposed to be a 3x2 matrix) ....[2 -3] Find (a) Ker(T) (b) nullity(T) (c) range(T) (d) rank(T) Ans: (a) {(0,0)} (b) 0 (c) {(t,0,s) | t,s real} (d) 2 I'm not exactly sure how to do it. The way he does it is a bit confusing and I dont understand it. EDIT: Not sure why it is showing both as number 1. The 2nd number 1 should be number 2 but its not changing so yea.

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Calculus Help? Hi, I kind of needed help with these Calculus problems. Not really sure how to even do them so if you can help I would appreciate that. 1. Find the centroid of the region bounded by y=sinx and y=0 between x=0 and x=4 2. Find the arc length of the graph y=sqrt(x) between x=0 and x=4 3. Not really sure how to write out this integral problem but ill try Integral of ln5 to ln7 of e^(2x) / (sqrt( (e^2x) - (6e^x) + 5)) dx 4. How much work is required to pump the water out of the top of a half-full 10 foot long horizontal cylindrical tank that has radius 3ft? The weight density of the water is 62.4 lb/ft^3 For number 1 i found out M and x bar but i can't figure out how to do y bar. the rest I have no idea how to do.

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