b) Find a basis for null(A). What is the dimension of null(A)?

Q: Find a basis for the null space of A

A: Consider the given matrix, A=-1-22-124-42 Convert the matrix into Row Reduced Echelon Form. Apply…

Q: Find an orthogonal basis for Null C

A:

Q: Let Is S a basis for R³?

A:

Q: 7) Is the basis B = an orthonormal basis? If it's not, then can we make it to become one?

A:

Q: 4. Find a basis for R3 that contains the vectors (1, 2, 3) and (3, 2, 1).

A: Note : according to our Company guidelines we can answer only first question, please repost the…

Q: How are n, rank A, and nullity A related to each other how can one find a basis for Col A, Nul A,…

A: Write the relationship between n, rank A and nullity A. Also write a procedure to find a basis for…

Q: Find a basis for the null space of matrix A. A = 1 2 Basis is

A:

Q: Let A = 3.6 1 -8 Find an orthonormal basis of the image of A.

A:

Q: Explain why S is not a basis for M22

A: We have t.o show that why S is not Basis for M2,2: Concept: The dimension of a vector space V, is…

Q: Find a basis for the null space of A -3 6 -1 1 -7 A = 1 -2 2 -1 2 -4 5 8 -4 3.

A: Given    A=-36-11-71-223-12-458-4We first find reduced row echelon form of  A.      Applying…

Q: Write standard Basis of P4(x)?

A: P4(x) is a collection of polynomial degree atmost 4

Q: 13. Do the set of vectors S = { x²+2x-4, 6x² +7x+3, 2x²+x) a basis for P2? Refer to the definition…

A: The given set is;  S=(x2+2x-4, 6x2+7x+3,2x2+x).

Q: Explain why S is not a basis for P2.S = {2, x, 3 + x, 3x2}

A: From the given value for S to find the values for pi(x).

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

A: Basis definition:

Q: 14. Use the Gram-Schmidt process to transform the basis for the Euclidean space R" into an…

A: We have to transform the given basis into an orthonormal basis for ℝ3

Q: Let B= { }].[),A} be basis for IR Is B orthonormal ? O False O True

A: Applying orthonormal property we have

Q: 2. Find the basis for the nullspace of A, and the nullity and rank of A

A: This is a problem of linear transformation.

Q: Find a basis for R2 that includes the vector (2, 2).

A:

Q: a. Use the Gram-Schmidt algorithm to convert the basis 1 1 3 into an orthogonal basis for R³.

A:

Q: Let B= { be basis for IR Is B orthonormal ?

A: Given B=3-30,22-1,114 be the given basis for ℝ3.

Q: 3) li) Find the dual basis {l, l} of the standard basis of IR". (i) Fiod th

A: Since you have asked more than one question, we will solve first one for you. If you want other…

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

A:

Q: Is it true that there is a basis for R^4 that consists of five vectors?

A: False. First I recall you what is the definition of basis. set B of vectors in a vector space V is…

Q: Explain why S is not a basis for P2.S = {−x, 4x2}

A: Given: S={−x, 4x2} To Explain: Why S is not a basis of P2.

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: Let }].,)} 3 B = { 1.E be basis for IR %3D 2 Is B orthonormal ? False True

A:

Q: is not a basis for R2. 4, 3), (8, 6)} rly dependent. ot span R2. urly dependent and does not span

A: We have to choose the correct answer from the given options according to the given information

Q: snip

A: Let S=0101,1101 As the dimension of M22 is 4. Also, it has 4 elements, and so it is linearly…

Q: ind a basis for the column space of -1 -1 0 -4 2 A = 3 -3 -2 -2 0 6 Sasis =

A:

Q: Let B= { [}].9Y be basis for IR. Is B orthonormal ?

A:

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

A:

Q: ind a basis for the nullspace of the matr

A: Given,         A=13-2501-12-2-64-10

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

A: We have given a set of the matrices;

Q: 4. (a) Use the Gram-Schmidt process on the basis {(1,2,3), (1, 1, 2), (2, 3, 1)} to find an…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: I Let 6 A = --2 -2 -4 -2 -2 -4 Find a basis for the null space of A. {

A: Let us consider matrix A of order n x m. The null space of matrix A is defined as: Null(A)=x∈Rm|Ax=0…

Q: Apply Gram-Schmidt method to change {{:)} into an orthonor- mal basis {u¡, u2} of R² .

A: We have to find the orthonormal basis for the given set.

Q: 5. Find a basis of R' containing the vector (1, 1, -2)' and (1, 2, -1)".

A:

Q: 12. The et 5 - {; 96 1A}- is: a. a basis of M22- b. not a basis of M2,2.

A: The standard basis of M2,2 is: e1=1000 ,   e2=0100 ,     e3=0010 ,    e4=0001

Q: How is the basis {lk} picked?

A:

Q: Let 1 A = 9 Find an orthonormal basis of the row space of A

A:

Q: 9 - - Let 1 3 5 A = -1 5 4 9 2 4 6 10 Which one is a basis for the column space, C(A), of A

A:

Q: 2 Find a basis for the column space of A = 9. 7 -5 {[ 2 Ex: 5 Ex: 5 -5

A:

Q: How would you represent it in Basis 2?

A:

Q: Explain why S is not a basis for P2.S = {1 + x2, 1 − x2}

A: Given: S = {1 + x2, 1 − x2}

Q: Determine whether or not S = {x² +1, x+ 2, –x² +x} is a basis for P2.

A:

Q: 39. Find an orthonormal basis 1, 2, 3 of R³ such that (G) span

A: Given,                        spanu1→=span123and        spanu1→, u2→=span123, 11-1

Q: - Let 3/2 U2 = U3 a. Show that {u1, u2, u3} is an orthonormal basis for R³.

A:

Q: be basis for IR? Is B orthonormal ?

A: We have to check whether B is orthonormal or not. Orthonormal means that each pair of vectors must…

Q: Determine a basis for the null space of A. 1 1 2 2 3 3 2 2 4 4 5 5 A = 0 0 0 0 1 1 1 1 2 2 2 2 1 2 1…

A: Null space of a real matrix A of size m×n is the set of all vector X∈ℝn such that AX=0. That is…