As per last week, we can put up our answers for those who want to redo. 1. A polynomial space in a variable is the linear combination of all possible real number multiples of that variable raised to all possible non-negative integers allowed within the defined space (ie P2(t): allows 0,1,2 as exponent integers). ex) t + 1, 2t 2. *swap order of equations, *multiply any equation by a scalar, *add any scale multiple of one equation to another 3. 2y - z = 1 (1) x - y + z = 1 (2) 2x + y + 2z = 2 (3) (3) = (3) - 2*(2) => 3y = 0 (1) = (1) - 2/3*(3) => -z = 1 *swap (2) with (3) new set -z = 1 3y = 0 x - y + z = 1 ==>>> (2,0,-1) 4. 2x - 2y = 4 (1) 4x + ay = b (2) so for there to be infinite answers (2) needs to be a scale multiple of (1) therefore, a = -4, b = 8 for there to be no solutions the lines need to be parallel, but not the same line therefore, a = -4, b != 8 for there to be one solution the lines need to intersect only once, I just made them orthogonal, a = 4, b = 8 => this makes then have a slope of 1 and -1 respectively and cross the y axis at -2 and 2 respectively making the solution (2,0) 5. A set of points with infinite number of of best fit would be any one point twice... I used {(2,1),(2,1)} SUMx = 4, SUMy = 2, SUMx^2 = 8, SUMxy = 4 2b + 4m = 2 (1) 4b + 8m = 4 (2) equation (2) is a scale multiple of (1) therefore infinite solutions
Posted on: Thu, 13 Feb 2014 06:03:05 +0000
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