Suppose a₁, 2², 23, 24, and a5 are vectors in R ³, A = (a₁ | a₂ | a3 | a | a5), and 1 0 00 rref(A) = a. Select all of the true statements (there may be more than one correct answer). A. span{a₁, a2, a3, a4} = R³ | B. span{a₁, a2, a3 } = R ³ | C. {a₁, a₂ } is a linearly independent set ☐D. {a₁, a₂ } is a basis for R ³ □E. {a₁, a₂, a3, a4} is a basis for R ³ F. {a₁, a₂, a3} is a linearly independent set |G. {a₁, a₂, a3 } is a basis for R ³ | H. span{a₁, a₂} = R³ |I. {A₁, A₂, A3, A4} is a linearly independent set 0 0 1 0 1 Y 7 22 -1 1

Q: If         →                    AB = (−5, 4) then 4 is the _____ of the vector.

A: We know in a vector of the form (a, b); a is the x-component and b is the y-component of the vector.

Q: Perform the following steps in R. Answer the questions in parts where there are questions. Attach R…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Let W be the set of all vectors Select an Answer ✓ 1. V= Determine whether each of the following…

A: Given that W be the set of all vectors xyx+y with x and y are real. The given vectors, 1.v=-507 2.…

Q: If a,b,c are vectors such that a.b=a.c,a×a=a×c, then show that b=c

A: Given, a,b,c are vectors such that a·b=a·c, a×a=a×c To prove: b=c

Q: 6. Create a two vectors x and y, vector x from 1 to 10 and vector y from 10 to 1 then a. Sum the two…

A: According to the given information it is required to form two vectors x, and y from 1 to 10 and from…

Q: Suppose a1, a2, a3, a4, and a, are vectors in R°, A = (a1 | a2 a3 a4 a5), and 0 0 0 1 0 [1 -5 5…

A:

Q: 2. 4 7 X•w Compute w • w, x•w, and using the vectors w=-1 and x = w•w - 5 3 w•w = (Simplify your…

A:

Q: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

A:

Q: Given the vectors (1 10), (0 2 3), (1 2 3) in R3. Given vectors are linearly independent. Select…

A:

Q: For any three vectors a, b, and c, we have a x (b x c) (a x b) x c. اختر احدى الدجابات True False

A:

Q: A vector is written as aî + bĵ. What form is that?

A: A vector is written as aî + bĵ.

Q: Find vectors v and w so that v+w= (4,5,6) and v-w=(2,5,8). This is a question with____ unknown…

A: Addition of vectors

Q: Use the vectors a = [-1,0,1], b = [1,-1,5], and č= [0,-1,-2] to prove that a(bxč) # (åxb)xč

A: The answer is given below:

Q: Given that 7 write 3 5 7 3 5 -2 2 3 7 -1 2 2 3 3 125 100 010 -5 001 3 as a linear combination of the…

A:

Q: Let u = 6 - 1 and v= 6 Show that a a -[:] k Let b = k How can it be shown that a vector b is in Span…

A:

Q: Is w in {V1, V2, V3}? Type "yes" or "no". How many vectors are in {V1, V2, V3}? Enter "inf" if the…

A:

Q: Suppose a₁, 2², 23, 24, and a5 are vectors in R ³, A = (a₁ | a₂ | a3 | a | a5), and a. Select all of…

A:

Q: Suppose a vector w R³ can be written as w = 5v₁ - 3v2 + 7v3, where V₁, V2, V3 are vectors in R³.…

A: Explanation of the answer is as follows

Q: Suppose a1, a2, a3, a4, and ag are vectors in R³, A = (a1 | a2 | a3 | a4 | a5), and [1 0 -5 5…

A:

Q: That is not correct. The first Vector answer is [-2/3, -1/3, -2/3] (column wise format.)

A:

Q: Select the statement(s) that is/are true. For any vectors a and b, if a x b = 0 then a = 0 or b = 0.…

A: Given query is to choose correct statements

Q: 2. Let A = a₁ + a2j + a3k and B = b₁i + b₂j + b3k. Then (A × B) . j is equal to a) a2bვ — a3b2 b)…

A: A=a1i+a2j+a3k B=b1i+b2j+b3k.

Q: "Given that 3 -4 = 5 -3+ 2 5 ܐ write 3 as a linear combination of the vectors -2 + 5 -3 -2 5 -4 1 2…

A: Here , a vector is given and now we have to represent it as a linear combination of three vectors .

Q: For each pair of vectors in i-iii, find the following: e. ||ū|| and ||3|| b. and ||ū|| |||| f. Ili2…

A: Since you have asked a question with multiple subpart here we will solve the first three subparts…

Q: Which of the following sets of vectors are orthogonal? O a. 5 3 4 2 -4 -3 -7 06 300 4 -5 -2 6 -6 360…

A: this is question of algebra here vector is given we have to check that this are orthogonal or not…

Q: Let A = 16 64 - 4 16 and w= Determine if w is in Col(A). Is w in Nul(A)? Determine if w is in…

A:

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

A:

Q: 2. If A = 2a, + 0.3a, – 1.5a, and B = 10a, + 1.5a, - 7.5a,, Show that A and B are dependent vectors.

A: The solution is given as

Q: draw the vector -u+ 2v + 4w

A:

Q: Consider B= {(4,6, c-1), (2, 3, 2c), (1, -1, c)} a set of vectors from R³. What are the values of c…

A:

Q: Suppose that the vectors and are equal. What is a? O O O O 3 a-b] a 2 a 2 512 502

A: given   a+b2=3a-b