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How do you find the matrix corresponding to a transformation?

Let's say that T is a transformation of the two dimensional plane. Remember that we have the two standard unit vectors (1,0) and (0,1). These are, respectively, the unit vectors pointing in the positive dire...
RF
3121 Views

Find the general solution to the differential equation: d^2y/dx^2 - 8 dy/dx +16y = 2x

d 2 y/dx 2 - 8 dy/dx +16 y = 2x Auxiliary Equation: m 2 - 8m +16 = 0 (m - 4) 2 = 0 m = 4 (repeated root) Complimentary function : y = (A+Bx)e 4x Particular integral : try y p = ax + b dy p /dx = a d 2 y p /d...
OF
9363 Views

P(A)=0.2, P(A|B) = 0.3 and P(AuB)=0.6. Find i P(B) ii P(B'|A')

i. P(AuB) = P(A) + P(B) - P(AnB) P(AnB) = P(A|B)P(B) = 0.3P(B) P(AuB) = P(A) + 0.7 P(B) --> 0.6 = 0.2 + 0.7 P(B) --> P(B) = 4/7 ii. P(B'|A') = P(A'nB')/P(A') P(A'nB') = 1 - P(AuB) P(B'|A') = 0.4/0.8 = 1/2
WS
9960 Views

How do you calculate the cross product of two vectors?

To calculate the cross product of two vectors you take the coordinates of vector 1 which are (x 1 ,y 1 ,z 1 ) and the coordinates of vector 2 which are (x 2 ,y 2 ,z 2 ) and put these coordinates into a 3x3 m...
MK
3805 Views

Find the area of the surface generated when the curve with equation y=cosh(x) is rotated through 2 pi radians about the x axis, with 2<=x<=6

Use the formula for the surface area of revolution, which requires dy/dx. So find dy/dx = sinh(x) and substitute dy/dx and y into the formula with the limits provided in the question (2 and 6). Then evaluate...
JH
5357 Views