所屬科目：主題課程專用
(5%) Let For what valuc(s) of h is b in the planc spanned by al and az? (A) 0 (B) -10 (C) 16 (D) -17 (E) 20
Which of the following sets is basis (are bases) for R3? (A){10,1,0]T,[0,0,1]T,[1,0,0T}. (B){-2,4,-6]T,[1,-2,3]T}. (C){|0.14,0, -0.1]T, [-1,-0.2,0.4]T,[0.5,0.5,-1)T} (D) {1-1,2,3]T, [8,-7,6]T, [4,-2,3]T,[9,0,5]T}, (E) None of the above are true.
(5%) Find the dimension of the subspacc (A) 2 (B) 3 (C) 4 (D) 1 (E) 0
(5%) Which of the following is true? (A) Every nonzero subspace of Rn has a unique basis. (B) Every subspace of Rn has a basis composed of standard vectors. (C) The column space of an m✖ n matrix is contained in Rm. (D) If V is a subspace of dimension k, then every generating set for V contains exactly k vectors. (E) The pivot columns of a m ✖ n matrix A form a basis for the column space of A.
Consider the vector space S consisting of all degree-2 polynomials with real coefficients, ie., polynomials in the form of c0 +c1t +c2t2. Define the inner product between two vectors as c2d2. Which of the following statement is/are true? (A). The dimension of S is 2. (B). The polynomials 1 + t, t and 1 + t2 are linearly independent. (C). The set{1 + t, t, 1 + t2} can be a basis for S. (D). The two polynomials 1 - 2t + t2, and -1 + 2t - t2 are orthogonal to cach other. (E). None of the above is true.
Find a basis of U, if exist, U ={f(x)|f(x)=a+bx+cx2+dx3},p3 =span{1,x,x2,x3}.(10%
(A) f(2)=0(B)f(1)=5(C)a+b=c+d, a=2d
Find the basis of the vector space V= (5%)
(a) (4 points) Choose a subset of which forms a basis for V.
a) (5%) Find an orthonormal basis for the subspace of R3 spanned by .
b. (5 points) Prove that B = is a basis of V.
(5 points) Prove that B'= is a basis of V.
阿摩線上測驗
登入
阿摩線上測驗
登入
For what valuc(s) of h is b in the planc spanned by al and az?
(A) 0
(B) -10
(C) 16
(D) -17
(E) 20
(A) 2
(B) 3
(C) 4
(D) 1
(E) 0 
c2d2. Which of the following statement is/are true?
(A). The dimension of S is 2.
(B). The polynomials 1 + t, t and 1 + t2 are linearly independent.
(C). The set{1 + t, t, 1 + t2} can be a basis for S.
(D). The two polynomials 1 - 2t + t2, and -1 + 2t - t2 are orthogonal to cach
other.
(E). None of the above is true.
(5%)
which forms a basis for V.
.
is a basis of V.
is a basis of V.