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研究所、轉學考(插大)◆工程數學
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110年 - 110 國立中央大學_碩士班招生考試_通訊工程學系/不分組(一般生)：工程數學#105325
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(b)(5%)
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69.一年好景君須記，最是橙黃橘綠時是指什麼季節?__ __季
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1. (10%) Let A and B be 3 ✖3 matrices with det(A) = 5 and det(B) = -6. Find the value of: (a) (5%) det(2AB)
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(a) (5%) If Ax = Bx for some nonzero vector x, then the matrices A and B must be equal.
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(b) (5%) If A is row equivalent to the identity matrix and AB = AC, then B must equal C.
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(a) (5%) Use the Gram-Schmidt process to find an orthonormal basis for the column space of A.
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(b) (7%) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular.
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(c) (8%) Solve the least squares problem Ax = b
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4. (10%) Consider the matrixwith parameter x. Specify all numbers x, if any, for which A is positive definite. Explain your answer.
#447118
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