Let u,- 2 , and u2 Select all of the vectors that are not in the span of sui, u2
ID: 3114427 • Letter: L
Question
Let u,- 2 , and u2 Select all of the vectors that are not in the span of sui, u2) A. The vector-93+72is not in the span. 6* 3+4 6 * 2 B. The vector is not in the span C. The vector3is not in the span. 0 D. The vector 0is not in the span. 0 E. The vector 0is not in the span F. The vector 73 is not in the span G. The vector 2is not in the span. H. All vectors in R3 are in the span I. The vector 9372is not in the span. 95 1 J. The vector 1 is not in the span K. We cannot tell which vectors are in the spanExplanation / Answer
A. -9(9,3,5)T+7(3,2,1)T= -9u2+7u1 being a linear combination of u1 and u2, is in span{u1,u2}.
B. The given vector is (22,12,6)T . Let A be the matrix with u1, u2 and this vector as columns. The RREF of A is I3. Therefore, the given vector cannot be expressed as a linear combination of u1 and u2. Therefore, the given vector is not in span{u1,u2}.
C. The given vector is (9,3,5)T = u2. Therefore, the given vector is in span{u1,u2}.
D. Let A be the matrix with u1, u2 and the vector (0,0,0)T as columns. The RREF of A is
1
0
0
0
1
0
0
0
0
Thus, the vector (0,0,0)T cannot be expressed as a linear combination of u1 and u2. Therefore, the given vector is not in span{u1,u2}.
E. Let A be the matrix with u1, u2 and the vector (1,0,0)T as columns. The RREF of A is is I3. Therefore, the given vector cannot be expressed as a linear combination of u1 and u2. Therefore, the given vector is not in span{u1,u2}.
F. 7(9,3,5) = 7u2 is apparently in the span{u1,u2}.
G. The given vector is (3,2,1)T = u1 is apparently in the span{u1,u2}.
H. Several vectors e.g. (0,0,0)T and (1,0,0)T are not in the span{u1,u2}. Therefore, all vectors in R3 cannot be in the span {u1,u2}. Also, any basis for R3 will have a minimum of 3 vectors.
I. The given vector is (-81,-27,-44)T+(21,14,7)T = (-60, -13, -37)T. Let A be the matrix with u1, u2 and the vector (-60,-13,-37)T as columns. The RREF of A is is I3. Therefore, the given vector cannot be expressed as a linear combination of u1 and u2. Therefore, the given vector is not in span{u1,u2}.
J. Let A be the matrix with u1, u2 and the vector (0,1,0)T as columns. The RREF of A is is I3. Therefore, the given vector cannot be expressed as a linear combination of u1 and u2. Therefore, the given vector is not in span{u1,u2}.
K. All the vectors which can be expressed as linear combinations of u1 and u2 , i.e. as au1 +bu2, where a and b are arbitrary scalars ,are in span{u1,u2}.
1
0
0
0
1
0
0
0
0
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.