The vectors B form a basis. Find a vector x given the B-coordinates of x are 3 [2] [x]R =

Q: Find the coordinate vector of p relative to {p,» P;» P3} for P,. the basis S =

A:

Q: { be a basis for R? . Find the vector æ if [æ]R =| 3 Let B 8 x = x = 6. x = x = H 00

A: Given that B=11,21 be the basis for R2. We have to find vector x if xB=23. Since, xB=23 Hence,…

Q: Find the coordinate vector [x]R of x relative to the given basis B= {b,. b2, bg}.

A: Here we have to find the coordinate vector [X]B of X relative to basis B.

Q: a' Find the value of a for which S forms a basis for R3.

A:

Q: Which of the following vectors form an orthogonal basis? BBE • BBA 2 3 [0 a) 1 b) 2 3 2 c) 12 d)…

A:

Q: Which of the following vectors form an orthogonal basis? 2 [0] T- 1] 3 го а) -1 4 b) -2 3 剛 2 -2' 3…

A:

Q: 4. Find a basis of each vector space below and hence write down the dimension of the space. You do…

A:

Q: 4. In each case, check that {v1, ..., Vn} is a basis for R" and give the coordinates of the given…

A: According to our guideline, gave importance on student requirement solved subpart a and c. If you…

Q: Which of the following vectors form an orthogonal basis? a) b) Q 12 d) None of these :Select one C a…

A:

Q: Find the coordinate vector of P relative to the basis S = {p1.P2;P3} P1 = 1 +x+ x², p2 = x + x², p3…

A: Write p as linear combination of p1 p2 p3 Then the scalar in linear combination is form coordinate…

Q: Consider the basis D = {(1, 1, -1), (2, 1, 3), (-1, 2, 1)} of R3 and the vector v = (1, 1, 1) in R3.…

A:

Q: Find the coordinate vector [x]B of x relative to the given basis B= {b1, b2} 3 3 b, , b2 - 7

A:

Q: 7. Let S be the set S = a) Show that S spans R3 and find a basis for R3 contained in S. b) What are…

A: Given :  The given set is,   S = 1-20, 012, -568, 1-21  To find : (a) We have to show that  S spans…

Q: Find all values of a for which the given vectors form basis for R' a? u = V = and w = a 1 2

A: given vectors u=a201 , v=0a2  and w=101 claim- find all the values of a for which the given vectors…

Q: a) Find the standard coordinate basis for the and -1] [3 B, = -1 b) What is the coordinate basis of…

A: Given: a)  The given details: xyB1= 2-1B1= 3-421 b)  B2= -1420

Q: ind the coordinate vector [x]g of x relative to the basis 1 B = X = -2

A: Coordinate vector of the given vector

Q: Find the vector x determined by the given coordinate vector [x]R and the given basis B. - 1 1 3 - 2…

A: To find  The vector X determined by the given coordinate vector [X]_B and the given basis B.

Q: Find the coordinate vector of P relative to the basis S = {p1.P2,p3} P1 = 1 + x + x², P2 = x + x²,…

A: Given that , S=p1,p2,p3p1=1+x+x2 , p2=x+x2 , p3=x2 , p=5-x+8x2 PS=?

Q: Do the following vectors form a basis for R? O a. Yes, the vectors form a basis for R2 O b. Cannot…

A:

Q: The set B = is a basis for R2. Find the coordinates of the vector x = -6 relative to the basis B.…

A:

Q: 11. The vectors 03 and a. form a basis for b. are orthogonal C are both of the above

A:

Q: Find the coordinate vector [x]B of x relative to the given basis B= {b1,b2,b3}. 1 3 2 b, = - 1 b2 =…

A:

Q: Given the basis B = the basisi B | {Q.B]} Find the change of coordinates matrix from the standard…

A: We find required matrix.

Q: Given the ordered basis B = {p1 =1– 1, P2 = 4 – 7x find [p]B, the coordinates of p = -7+ 10x with…

A: Follow next step

Q: Find the vector x determined by the given coordinate vector [x]R and the given basis B. -4 [x] B% =…

A:

Q: Find a basis for S. a + 9b a - b , where a and b are real numbers. S is the set of vectors of the…

A: A basis for a vector space is a linearly independent set which spans the space.

Q: 4. Find a basis of each vector space below and hence write down the dimension of the space. You do…

A: We have been given 4 vector spaces and we need to determine the Basis in each case.

Q: ,B = the standard basis, C - {[; -}-[; :)-8)-[: 9]} in 22 (a) Find the coordinate vectors [A] and…

A: The standard basis B for M22 is {e1,e2,e3,e4}.

Q: Find the coordinate vector [x]R of x relative to the given basis B= {b1.b2}. 3 b1 b2 - 2 X= 4 [x]g =

A:

Q: In the vector space of polynomials of degree at most two, coordinates of the vector p()=5+x+5x2 in…

A: Given p=5+x+5x2and Basis B={e1 =1+x, e2=x+x2 ,e3=2+x}

Q: 7. ) Given vectors v1 (3,0,0), v2 = (1,2,0), and v3 = (2, –4,5). a) Are the vectors linearly…

A: The objective is to determine whether the given vectors are linearly independent or linearly…

Q: 2) Find the coordinate vector [x]p of x relative to the basis B={b1, b2}: [-3] bị = G.b2 = x =G

A:

Q: Consider the basis 8-{(!). (3)} 1 2 B = 2 of R2. What is the coordinate vector of (1) with respect…

A: Given basis is B=12,25 We have to find the coordinate vector of x¯=21 Let the coordinate vector of…

Q: B = {3 – 3x, 9 – 2x – 9x², 13 – 4x – 12x?} is a basis for P2. The coordinate vector of p(x) = 4 + 2x…

A: We have to find the coordinate vector of P(x)=4+2x-6x2. w.r.t the basis…

Q: B = is a basis for R2. Find the coordinates of the vector x = relative to the basis B. -14 [x]B |

A:

Q: Find the vector x determined by the given coordinate vector [x]gand the given basis B. B= , [x]g =

A:

Q: Find all values of a for which the given vectors form basis for R' a² u = v = and w = a 1 2

A: Basis of a vector space: A set S⊂V(F) is said to be basis of vector space over field F if it…

Q: Given vectors v1 = (3,0,0), v2 = (1,2,0), and v3 = a) Are the vectors linearly independent or…

A:

Q: Find a basis for the set of all 2 vectors of the form a – 2b + 5c 2a + 5b – 8c (Be careful.) -a – 4b…

A:

Q: Find the coordinates of x in the ordered basis B = (a, b). %3D [2]B =

A: Consider the vectors: a=-7-2, b=7-2 and x=-2-5. As the ordered basis is B=a, b=-7-2,7-2, we have…

Q: Given vectors v1 = (3,0,0), v2 = (1,2,0), and v3 = (2,–4,5). %3D a) Are the vectors linearly…

A:

Q: Let B = {b1, b2, b3} be a basis of R where 3 bị -4 b2 b3 = Let v = -4 . Find the vector v]R of…

A:

Q: a) Find the coordinate vector of x = of R³. To with respect to the ordered basis *- {0-1-8} E [x] E…

A: as per the guidelines I am answering only first question (a) Let the coordinate vector of x=2-40…

Q: 1 with respect to the basis 25 Find the coordinate vector of -3 -17 {[ 1 2 1 2 0 B = 0 2 1 1

A:

Q: The vectors 02 = 6. 03 = form a basis for R' if and only if k +

A: Given vectors are: v1→=4-10,v2→=-666,v3→=24k We have to find the value of k when the vectors form…

Q: - {EE} is a basis for R2. Find the coordinates of the vector x = relative to the basis B. -14

A:

Q: Show that the given vectors form an ortho­gonal basis for R2 or R3• Give the coordinate vector [w]of…

A: Orthogonal basis:        Let v1,v2,.....,vn be linearly independent vectors in Rn, if v1,v2,.....,vn…

Q: 30 175 The vectors B = form a basis. Find the B-coordinates of x = [z]p =

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.