首頁 > 線上測驗 > 100年研究所工程數學歷屆試題(工數1)電機所.電子所. 電信所.光電所.通訊所(二年期) > 100年國立雲林科技大學資工電光所工程數學
A and B are 3×3 matrices and | A |= −3 , | B |= 2 .
Which statements are correct?
| AB |= −6
| 2AB−1 |= −6
| (A2 )t |= −9
| (At )2 |= 9
| (A2B−1)t |= −18
Consider the two vectors, (1,2,−1) and (3,1,0)
(1) Find the norms of the two vectors.
(2) Normalize the two vectors.
(3) Find a vector that is orthogonal to the two vectors.
(1) Find its eigenvalues.
(2) Find the corresponding normalized eigenvectors.
(3) Find the matrix A10 .
Asus and Acer are competing for customers at notebook market. A study has been
made of customer satisfaction with the various companies. The results are expressed
by the following matrix R . The First column of R implies that 75% of those
currently using Asus notebook are satisfied and intend to use Asus next time, while
25% of those using Asus are dissatisfied and plan to use Acer next time. There is a
similar interpretation to the second column of R . If the current trends continue, how
will the customer distribution eventually settle?
Gauss-Jordan elimination.
Determine the equation of the polynomial of degree two whose graph passes through
the point (1, 6), (2, 3), (3, 2).
Determine the inverse of each of the following matrices, if it exists, using the method
of Gauss-Jordan elimination.
Solve the following problems.
Prove that the transformation T : R2 → R2 defined by T(x, y) = (3x, x + y) is linear.
Find the images of the vectors (1, 3) and (−1,2) under this transformation.
Consider the linear transformation T defined by each of the following matrices.
Determine the kernel and range of each transformation. Show that dim ker (T) +dim
range (T) = dim domain (T) for each transformation. (Note that the abbreviations of
dim and ker denote dimension and kernel, respectively.
可觀看題目詳解,並提供模擬測驗!(免費會員無法觀看研究所試題解答)