Explain why S is not a basis for M, 2. -{{::}{:}} 0 1 1 0 10 0 1 S is linearly dependent. s does not span M, 2. O S is linearly dependent and does not span M2 2

Q: Explain why S is not a basis for R³. S = {(8, 6, 13), (6, 1, 4), (3, 1, -5), (0, 8, 3)) OS is…

A: Definition of a basis of ℝ3 : A set S is said to be a basis of ℝ3 if  i) It is linearly independent…

Q: Explain why S is not a basis for M2,2.

A: Let's check if S is linearly independent or not. S will not be linearly independent if for some…

Q: snip

A: The basis in n-dimensional space is called the ordered system of  linearly independent vectors. Let…

Q: Explain why S is not a basis for P. S = {1, 8x, -4 +x², 9x} O sis linearly dependent. O s does not…

A:

Q: Explain why S is not a basis for R². S = {(-6, 2)} OS is linearly dependent. S does not span R². OS…

A:

Q: Explain why S is not a basis for P,. S = {1 – x, 1 - x², -1 - 6x + 7x2} O s is linearly dependent. O…

A: Given that - S = {1-x, 1-x², -1- 6x + 7x²}

Q: Show that the set S = {1,-1), (1,1)} form a basis for R? Support your answer with an explanation or…

A:

Q: Explain why S is not a basis for R2. S = {(-4, 9), (0, 0)} O sislinearly dependent. O sdoes not span…

A:

Q: Consider the following. 1 -1 V = M, 22, B = Complete the following statements. The elements of set B…

A: Elements of a set is set to be linearly independent if linear combination of the elements is 0 if…

Q: Explain why S is not a basis for R3.S = {(7, 0, 3), (8, −4, 1)}

A: Basis definition:

Q: Explain why S is not a basis for P2. S = {1, 6x, –7 + x2, 9x} O Sis linearly dependent. O s does not…

A:

Q: It can be shown that the vectors u1 = (2,−3, 1), u2 = (1, 4,−2), u3 = (-8, 12,−4), u4 = (1, 37,−17),…

A: A basis is a subset of a vector space that spans the vector space and is linearly independent.

Q: Explain why S is not a basis for P,. S = {1 - x, 1 – x?, -1 – 2x + 3x?} O sis linearly dependent. O…

A:

Q: Explain why S is not a basis for M, O sis inearly dependent. O s does not span M.2 O sis linearly…

A: We can solve this as follows:

Q: §8.3, Exercise 1. Let wi = (1,4) and w2 = (-2, 1). %3D Find the coordinates of v = (-1,32) in the W…

A:

Q: Explain why S is not a basis for M2,2- s={: :}[::} 1 0 0 1 O sis linearly dependent. O s does not…

A:

Q: Show that the set S= {(-2,-4), (1, 2)} is the basis of R2 or not?

A:

Q: Explain why S is not a basis for R2.S = {(4, −3), (8, −6)}

A:

Q: Explain why S is not a basis for M2,2" 0 1] 1 0 0 1 1 0 O sis linearly dependent. O s does not span…

A: Here given set as S=0101, 1010 Now a, b lies in the field…

Q: Let A = {v1, v2,.., Vn} be a basis for FV and n > 2. Is B = {v1 + V2, , V2 + V3, ..., Vn + v1} also…

A:

Q: Explain why S is not a basis for P2. S = {1, 6x, –9 + x², 7x} O Sis linearly dependent. O S does not…

A:

Q: Let {e1, e2, ē3, ē4, ē5, ē6} be the standard basis in Rº. Find the length of the vector 4ē4 + 4ē, –…

A: Consider the given standard basis in R6 as, e1→,e2→,e3→,e4→,e5→,e6→ As we know that standard basis…

Q: Explain why S is not a basis for R2.S = {(6, −5), (12, −10)}

A:

Q: 5. Consider the basis aj = (1, 2, 3), az = (2, 4, 5), and az = (3, 5, 6) for R] × 3. Consider t E…

A: Given α1 =1, 2, 3, α2 =2, 4, 5, α3 =3, 5, 6 is the basis of R1×3 So let α = α1, α2, α3 Let τ = α…

Q: ...... Explain why S is not a basis for M, 2. 1 0 0 1 Os is linearly dependent. O s does not span…

A:

Q: Let A = {v1, vz, - also a basis for pV? How about the converse, i.e. if B is a basis for FV, is A…

A:

Q: Explain why S is not a basis for M,2" 0 1 1 0 S = 1 0 0 1 O sis linearly dependent. O s does not…

A:

Q: Explain why S is not a basis for R3.S = {(1, 1, 2), (0, 2, 1)}

A: To determine: The set S is not a basis of R3 S = { (1, 1, 2), (0, 2, 1) }

Q: Find a standard basis vector that can be added to the set (v1, v2} to produce a basis of R^3.   v1…

A: The set (v1, v2} to produce a basis of R^3.       v1 = (1, -1, 0) and v2 = (3, 1, -2)

Q: Show that S = {(i, 0, 0), (i, i, 0), (0,0, i)} is a basis for C

A:

Q: 5. Determine whether the following three vectors v, = (1, 2, 3, 4), = (0, 1, 0, -1) and v, = (1, 3,…

A: To determine the given vectors form of basis for or not.

Q: Explain why S is not a basis for R2. S= {(3, 5), (1, 0), (0, 1)} O sis linearly dependent. O does…

A: The given set S=3,5, 1,0, 0,1

Q: Show that B = {v1=(1,0,0), v2=(3,7,-2), v3=(0,4,1)} is a basis for R3

A:

Q: b) Let v1 = (1,2,1), V2 = (2,9,0) and vV3 = (3,3,4). Show that S = (V1, V2, V3) is a basis for R³.…

A: Explained below...

Q: 2. Determine whether the set S = {(2, 0, 1), (2, -1, 1), (4, 2, 0), (-6, 2, 3)} a. Spans R3 b. Is…

A:

Q: 2.) Determine whether S = is a basis for R³. If it is write u = (6,3,6) as a linear combination of…

A:

Q: Explain why S is not a basis for M2,2.

A: We have given a set of the matrices;

Q: Let W¡ be the set: 1 Determine if W¡ is a basis for R³ and check the correct answer(s O A. W¡ is not…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Explain why S is not a basis for P2. S = {1, 6x, –5 + x², 8x} O sis linearly dependent. S does not…

A: Basis: A non-empty subset B of a vector space is basis if a) B is linearly independent b) B spans V.…

Q: 4 2 If a basis for R3 is B = and if a vector in the standard basis is i = |-4|, find its 5…

A: We know, The set B of vectors in a vector space V is called a basis if every element of V can be…

Q: Show that B = {1,1 – x,2 – 4x + x²,6 – 18x + 9x² – x³} is a basis for P3(R). Hint: Recall that…

A:

Q: Find a standard basis vector that can be added to the set {V1, v½} to produce a basis for R а. 0 —…

A: We have to solve given problem:

Q: The vectors e = and e2 are Select one: are the standard basis for R^2. O True False

A: Recall: Let V be a vector space . A linearly independent spanning set for V is called a Basis.…

Q: a)show that { d,b',7} it's a basis

A:

Q: If u =,x=(0,0,7,5,0) are linearly independent then they will form basis for RS. O True O False

A: A set of vector S is said to be basis of vector space of V iff 1) S is linearly independent  2) span…

Q: 1- The vectors x, = (2,1, -4), x2 = (-3,4,1) and x3 = (2, –1,3) in R3, are %3D A: represent a basis…

A:

Q: Explain why S is not a basis for M. 2,2' 1 1 S = 0 0 O is linearly dependent. O s does not span M2,2…

A:

Q: Let S = {1+4x– x², 2+5x+3x², 3x –5x², 3+15x +8x} . Does S span P,? Is S a basis for P, ? If not,…

A: