推 ketsu1109 :已收入精華區 03/19 22:50
課程名稱︰工程數學-線性代數
課程性質︰統一教學
課程教師︰馮世邁
開課學院：電機資訊學院
開課系所︰電機工程學系
考試日期（年月日）︰2009.03.19
考試時限（分鐘）：50
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Use of all automatic computing machines including calculator is prohibited
1. Let the matrix A and the vector b be respectively defined by
[ 1 2 -1 2 0 1] [2]
A = [a1 a2 a3 a4 a5 a6] = [-1 -2 1 2 0 3] , b = [6]
[ 2 4 -3 2 0 0] [3]
(a) (20%) Find the reduced row echelon form [R c] of [A b].
(b) (10%) What are the rank and nullity of A?
(c) (10%) Is the set {a1, a3, a6} linearly independent? Explain your answer.
(d) (10%) Is the equation Ax = b consistent? If it is, find its the general
solution in vector form.
(e) (10%) From the reduced row echelon form [R c], determine if the vector
b is in the span of {a1, a3, a4} or not? If it is, write b as a
linear combination of a1, a3, a4.
(f) (10%) From the reduced row echelon form [R c], can you find the reduced
row echelon form of the 3 × 4 matrix A' = [a1 a4 a3 a6]?
2. (20%) Let A = [a1 a2 a3 a4 a5 a6] be the 3 × 6 matrix defined in Problem
1. Choose 3 vectors from {a1, a2, a3, a4, a5, a6} to form an
invertible 3 × 3 matrix. Find its inverse.
3. (10%) Suppose that B and C are 3 × 3 matrices, and B is invertible. Find
the reduced row echelon form of (a) [B I3]; and (b) [C]
[B] (Express your
answer in terms of O, I3, B, B^(-1), and C).
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.239.197