Let A =b63-6 3 04 3 1and b =a₁+a3=a. Is b in {a₁, a2, a3}? [Select an answerb. How many vectors are in {a₁, a2, a3}? (Enter o for infinitely many.)c. Is b in Span{a₁, a2, a3}? Select an answerd. If b is in Span{a₁, a2, a3}, write b as a linear combination of a₁, a2, a3. Don't write anything if bis not in Span{a₁, a2, a3}.a₂+-27-27a₂+a3e. How many vectors are in Span{a₁, a2, a3}? (Enter ∞o for infinitely many.). Denote the columns of A by a₁1, a2, a3.f. Show that az is in Span{a1, a2, a3} by writing a3 as a linear combination of a1, a2, a3.a₁+a3

Answered: tA= -63 0 and b = 4 3 1 6 -27. . Denote…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4
Could a set of three vectors in R4 span all of R4? Explain. What about n vectors in Rm when n is less than m? Could a set of three vectors in R4 span all of R4? Explain. Choose the correct answer below. O A. No. The matrix A whose columns are the three vectors has four rows. To have a pivot in each row, A would have to have at least four columns (one for each pivot). B. No. There is no way for any number of vectors in R4 to span all of R4. OC. Yes. A set of n vectors in Rm can span Rm when n
d) the transpose of x. 2- If x= [2 8 5; 97 1], b=[2 4 5] find: a) find the maximum and minimum of x. b) add the vector b as a third row to x.
Please do last part
If A = [a1, a2, a3] has as columns the three vectors a1, a2, and a3. What is y = Ax,where x is a vector with three components, x1, x2, x3? Is y in the column spaceof A?
Defermine if the set of vectors is limeorly iedepandlant. -5 3 -4 (2) v = 3.8/10
State if the following statement is true or false. The set of vectors B={u= (2,7,3); v = (1,0,7) ;w=(3,7,-4)} spans R³. O True False
Express each column vector of AA as a linear combination of the ordered column vectors C₁, C2, and c3 of A. -6 A = 6 2 4 3 Enter first column as a linear combination of columns of A in terms of the vectors C₁, C₂, and c3: Enter second column as a linear combination of columns of A in terms of the vectors C₁, C2, and c3: Enter third column as a linear combination of columns of A in terms of the vectors C₁, C₂, and c3:
Suppose a₁, a2, a3, a4, and a5 are vectors in R ³, A = (a₁ | 8₂ | a3 | a | a5), and a. Select all of the true statements (there may be more than one correct answer). 3 A. span{a₁, a2, a3, a4} = R ³ 3 | B. span{a₁, a2, a3} = R³ C. {a₁, a₂} is a linearly independent set D. {a₁, a₂ } is a basis for R ³ 3 | E. {a₁, A₂, A3, A4} is a basis for R F. {a₁, a₂, a3} is a linearly independent set G. {a₁, a₂, a3 } is a basis for R ³ 3 3 H. span{a₁, a₂} R ³ = rref(A) = |I. {A₁, A₂, A3, A4} is a linearly independent set 9 1 0 0 1 0 0 -4 0 -1 1 1 NL 2 2
. Create a vector named prob18a that has 10 elements of which the first is 8, the increment is 7, and the last element is 71. Then, assign elements of prob18a to a new vector prob18b such that prob18b has 7 elements. The first 4 elements of prob18b are the first 4 elements of the vector prob18a and the last 3 elements of prob18b are the last 3 elements of prob18a. Do not type the vector elements explicitly.

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