## 4. Using the results of problem 3, what is the solution to the IBVP PDE 4, = 4 0

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# Advanced Math

## Two fair dice are thrown. Let A be the event the the first shows an odd number, B be the event that the second shows an even number, and C be the event the either both are odd or both are even.

## 1 -3 2 -6 If T is defined by T(x)=Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A-| 0 1-2 | and b-1-26 5-16 10 Find a single vector x whose image under T is b

Two fair dice are thrown. Let A be the event the the first shows an odd number, B be the event that the second shows an even number, and C be the event the either both are odd or both are even. Show that A, B, C are pairwise independent, but not independent. Are A …

EXPERT ANSWER 6 . Let the pre-image of (-6,-26,-2)T be x = (a,b,c)T where a,b, c are arbitrary real numbers. Then T(x) =Ax = (-6,-26,-2)T or, (a-3b+2c, b-2c, 5a-16b+10c)T = (-6,-26,-2)T . Hence, a-3b+2c = -6 …(1), b-2c = -26…(2) and 5a-16b+10c= 10…(3). The augmented matrix of the above linear system of equations is M (say)= 1 -3 2 -6 …