Dimension of basis of any subspace 2X3 matrix is equal to. . O a. 9 O b. 6 O c. 3 O d. NONE OF THESE ANSWERS O e. 15

Q: (2) Find a basis for the subspace W = {(a +c, 2a – b, 3a – 26 – c,b+ 2c) | a, b, c € R} of R.

A: We need to find the basis for the given subspace:

Q: 1. Find a basis for the vector subspace of 2 x 3 matrices given by а 6 c V := { : a + b+ c= 0, a = c…

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Q: The sets B={[1 2 2 1]T;  [1 0 2 0]T;  [2 0 4 -3]T} and B'={[0 2 0 1]T;  [2 1 4 -1]T;  [1 2 2n 4]T}…

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Q: 1. For each of the following matrices, determine a basis - and N(A"): 4 subspaces R(A"), N(A), R(A),…

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A: In order to find column space of matrix, firstly calculate the row echelon form of the given matrix.…

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A: For (a), Now, we need to find the basis. Here, u+v=0⇒v=-u and u-2w=0⇒w=u2. So,…

Q: Find a basis and the dimension of the given subspace of R4: a + c a – b b+c E R4 -a + b

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Q: Find a basis for the subspace а : a, b, c, d E R with 3a + b=0 and c+ d = 0 C W = 6. 6. d of R4.

A: Since 3a+b=0 Therefore b= -3a  And since  c+d=0  Therefore d= -c

Q: For the given subspace, H, (i) find a basis for the subspace, and (ii) state the dimension. 2c (а) Н…

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Q: 14. The vector x is in a subspace H with a basis B = {b₁,b₂}. Find the B-coordinate vector of x. (a)…

A: We can solve this as follows:

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A: According to the given information, it is required to tell which set among the given set is not a…

Q: Find a basis for subspace S of M2,2. s ={ [ ] : 4a – b = 2c + 2d ; a, b, c, d E R - C

A: We have to find basis of subspace S of M2x2 matrix.

Q: Find an orthogonal basis of the subspace of spanned by the vectors (a) (b) -2 (c) (d) 234

A: To find the orthogonal basis of the subspace of spanned by the vectors 234 and 123 Consider that the…

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Q: For an m x n matrix A, the column space is a subspace of Rn. True False

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Q: The solution space of the homogeneous linear system 0 0 Ax = 0, where A 1 2 0 is a subspace of R³.…

A: Given the homogeneous linear  system  Ax=0 , where  A=200120-352 Let   x=x1x2x3         x1 , x2 ,…

Q: A matrix A and its reduced row echelon form are given below. [1 0 8/5] 0 1 1/5 0 0 0 0 [1 2 2] 2 4 4…

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Q: Find an orthogonal basis of the subspace of spanned by the vectors 日目 4 (a) (b) (c) (d) 30 e.None of…

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Q: Is W a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that…

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Q: 4. Find a basis and the dimension of the subspace W of V = M22(R) spanned by %3D -5 2 -4 A = B = C =…

A: Given:          V = M2 × 2(ℝ) spanned by A = 1-5-42 ; B = 11-15 ; C = 2-4-57 and D = 1-7-51   To…

Q: 2. Consider the set of matrices W : b : а,b€ R a (a) Show that W is a subspace of M22. (b) Find a…

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Q: The sequence B = (|1 3)) is a basis for the subspace U = {{ r2| |r1 – 3r2 + 2r3 = 0}. 13 The vector…

A: We have to find the coefficient for linear combination

Q: (a) If S is the subspace of M6(R) consisting of all upper triangular matrices, then dim S = (b) If S…

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Q: Find bases for the four fundamental subspaces of the matrix A. 15 4 A = 0 2 0 N(A)-basis N(AT) =…

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Q: Let A be an m × n matrix (where m < n) whose rank is r.(a) What is the largest value r can be?(b)…

A: Given a matrix A of order m×n whose rank is r.

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Q: {] Find a basis for the subspace U = | a, b, c € R } of R³. Please justify your answer. -6

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Q: Find bases for the four fundamental subspaces of the matrix A. 189 A = 0 30 N(A)-basis N(AT) = %3D…

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Q: (b) Let A and B be 30 × 29 matrices. Show that there exists a vector c E R30 such that both the…

A: Question: Let A and B be 30x29 matrices. Show that there exists a vector c∈ℝ30 such that the system…

Q: If A is an mxn matrix, then the row space of A is a subspace of: O A. Rmn B. R". O C. R". n-m

A: Given that A is an m×n  matrix, then the row space of A is a subspace of :

Q: Find bases for the four fundamental subspaces of the matrix A. 1 4 9 A = 0 8 0

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Q: Find bases for the four fundamental subspaces of the matrix A. 0 11 A= 111 122 NA)-basis

A: Given: A=100011111122 To Find: NA basisNAT basisRA basisRAT basis

Q: Find a basis for the subspace W = {(a,b,c) ∈ R3 | b = 2a−3c}.

A: Given below the detailed solution

Q: Given A be a 2 x 2 matrix with the form listed below: A = [0 a          b 0]  , where V = M2,2.…

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Q: (a) The set V = || ER? : x = 0 or y = 0 } is a subspace of R2. (b) If A is a 3 × 3 matrix and ủ, v…

A: a) Given statement is V=xy∈ℝ2:x=0 or y=0 is a subspace of ℝ2. Given statement is False. A subspace S…

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Q: Given below is a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state…

A: Consider the row echelon form of the matrix, A=1324004-900040000 Considering the matrix Column 1,…

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A: We have given the basis   B=b1,b2where b1=21 , b2=-13   and we have a vector x = 49in a subspace H…

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Q: Let A and B be m x n matrices. Show that V = {x e R" : Ax = Bx} is a subspace of R".

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Q: Find a basis and the dimension of the column space of the matrix A, where 0 1 -2 1 A=| 5 2 1 -3 3 0…

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Q: Find bases for the four fundamental subspaces of the matrix A. 15 1] A = 0 2 0 N(A)-basis N(AT) =…

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Q: Which of the following sets are subspaces of Rª ? I. The solution set of the system Ar = 0, for a 4…

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

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A: Let β={ u1  ,u2  , ......., un } be an ordered basis for a finite dimensional vector space V then…

Q: Q7) Find a basis for the subspace and state the dimension.  {[2c a − b b − 3c a + 2b]:a, b, c in…

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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.