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amandapill
27.03.2020 •
Mathematics
Formulate the following problem as least squares problems. For each problem, give a matrixA and a vector b such that the problem can be expressed asargmin)‖Ax − b‖..(you are not asked to solve the problems. Just state define matrix A and vector b)a. minimize x/. + 2x.. + 3x3. + (x/ − x. + x3 − 1). + (−x/ − 4x. + 2).;b. minimize x8x + ||Bx − d||., where the p × n matrix B and the p-vector d are givenc. minimize ||Bx − d||.+2||Fx − g||.. The p × n matrix B, the × n matrix F, the p-vector d and the -vector g are given.
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Ответ:
a)![A=\left[\begin{array}{ccc}1&2&3\\1&-1&1\end{array}\right]](/tpl/images/0566/5639/5949e.png)
b)![||Ax-b||^{2} =(-bx_{2}+4)^{2} (-4x_{1} +3x_{2} -1)^{2} +(x_{1} +8x_{2} -3)^{2}](/tpl/images/0566/5639/0c5fb.png)
c)![A=\left[\begin{array}{ccc}0&6\sqrt{2} &0\\\sqrt{3} &3\sqrt{3} &0\\2&-16&0\end{array}\right]](/tpl/images/0566/5639/c19db.png)
Step-by-step explanation:
a) considering the equation:
Minimize![x_{1}^{2} +2x_{2}x^{2} +3x_{3}^{2}+(x_{1} -x_{2} +x_{3} -1)^{2} +(-x_{1} -4x_{2} +2)^{2}](/tpl/images/0566/5639/d7f99.png)
vector b
b) If Pxn is matrix B and p-vector d, we have:
minimize![(-6x_{2}+4)^{2} +(-4x_{1} +3x_{2} -1)+(x_{1} +8x_{2} -3)^{2}](/tpl/images/0566/5639/6aa81.png)
c) minimize![2(-bx_{2}+4)^{2} +3(-4x_{1} +3x_{2} -1)^{2} +4(x_{1} -x_{2} -3)^{2} -(6\sqrt{2}x_{2} +4\sqrt{2} )^{2} +(-4\sqrt{3} x_{1} +3\sqrt{3}x_{2} -\sqrt{3})^{2} +(2x_{1} -16x_{2} -6)^{2}](/tpl/images/0566/5639/56df0.png)
in matrix:
Ответ:
-4^0, 2^-3, (-3)^0, 5^1
Step-by-step explanation:
2^-3= 1/8 (the same as 0.125)
(-3)^0= 1
-4^0= -1
5^1 = 5
these numbers from lowest to largest would be -1, 0.125 (1/8), 1 and finally 5
making the answer -4^0, 2^-3, (-3)^0, 5^1