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無年度 - 主題課程_行列式和線性方程式：線性方程式#107934
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題組內容
Let A=
.For what values of Cdoes the equation Ax =B have
a) One solution.(7%)
其他申論題
(c) If L1 and L2 are both linear operators on a vector space V, then Li + L2 is also a linear operator on V, where L1 + L2 is the mapping defined by (L1+L2)(v)=L1(v)+L2(v)forallvV
#462717
(d) If N(A) = {0}, then the system Ax = b will have a unique least squares solution.
#462718
(e) If{u1, u2,... ,uk} is an orthonormal set of vectors inRnand U = {u1, u2,... ,uk} then UUT = In (the n x n identity matrix).
#462719
(15%) Let T:P2(R)＞ P2(R) be a linear operator that is defined according to T(g(x))=g(x)+ , in which P2(R) is a set of all polynomials with real-value coefficients and degree n, n=0,1,2. Please find the eigenvalues and the associated eigenvectors of the operator
#462720
b) No solution.(7%)
#462722
c) Infinitely many solutions. (6%)
#462723
Consider the following linear equation systems, express these equations as the matrix form Ax=b. Then find the solution of the vector x. (5%)
#462724
(a) (6%) Find the reduced row echelon form ofA.
#462725
(b) (3%) What are dimnensions of Col( A ), Row( A ), and Null( A )? (6 %) Justify your answers. 0 T
#462726
a) (5%) no solutions;
#462727
.For what values of Cdoes the equation Ax =B have
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.For what values of Cdoes the equation Ax =B have