Assignment_1 - of the other two types 6 Solve the following...

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Math 136 Assignment #1 1. Find the equation of the circle x 2 + y 2 + ax + by + c = 0 passing through the points (1 , 1), (5 , - 3), and ( - 3 , 3). 2. Find conditions on a so that the following system has (a) one solution, (b) no solution, or (c) infinitely many solutions. x + 2 y - 4 z = 4 3 x - y + 13 z = 2 4 x + y + a 2 z = a + 3 3. Find a , b and c such that x 2 - x + 3 ( x 2 + 2)(2 x - 1) = ax + b x 2 + 2 + c 2 x - 1 (Hint: Multiply through by ( x 2 + 2)(2 x - 1) and equate coefficients of powers of x .) 4. If ad = bc , show that a b c d has reduced row-echelon form 1 0 0 1 . 5. Show that any two rows of a matrix can be interchanged by using elementary row operations
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Unformatted text preview: of the other two types. 6. Solve the following system of non-linear equations for x and y : x 2 + xy-y 2 = 1 2 x 2-xy + 3 y 2 = 13 x 2 + 3 xy + 2 y 2 = 0 7. Solve the system for x , y and z where i is an imaginary number that satisfies i 2 =-1. x + 2 y + 2 z =-3 2 x + y + z = 0 x-y-iz = i 1...
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