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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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題組內容
3. (20%)
(a) (5%) Use the Gram-Schmidt process to find an orthonormal basis for the column space of A.
其他申論題
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)
#447111
(b)(5%)
#447112
(a) (5%) If Ax = Bx for some nonzero vector x, then the matrices A and B must be equal.
#447113
(b) (5%) If A is row equivalent to the identity matrix and AB = AC, then B must equal C.
#447114
(b) (7%) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular.
#447116
(c) (8%) Solve the least squares problem Ax = b
#447117
4. (10%) Consider the matrixwith parameter x. Specify all numbers x, if any, for which A is positive definite. Explain your answer.
#447118
(a)(4%) Find the probability that the smallest number drawn is more than or equal to 4.
#447119
(b)(4%) Find the probability that 8 is the largest number drawn.
#447120
6.(8%) We have three coins; the first two coins are fair and the last coin is two-headed. We pick one of the coins at random, and toss it twice. Heads show both times. Find the probability that the coin picked is fair.
#447121
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