What is the dimension of the following subspace U of R2x2 ? 3 U = span({ }) -2 -2

Q: 3. Determine whether the given set is a subspace of M2x2 with real entries. {6 ) la = b}.

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Q: 3. Let W = M2x2(C) with zero determinant. Show that W is not a subspace of V = M2x2(C).

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Q: Show that W = {(x1, x2): x1 ≥ 0 and x2 ≥ 0}, with the standard operations, is not a subspace of R2.

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Q: Find a basis of the subspace of R4 consisting of all vectors of the form ⎡ x1 −8x1+x2…

A: In this we have to find the basis of given vector subspace.

Q: Determine whether the subspaces are orthogonal.

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Q: Consider the subspace V of R4 given by 1 3 1 V = span || -1 1 1

A: Solution:-

Q: Q4(a) Define the null space of an m x n matrix A and prove that it is a subspace of R"

A:

Q: 2. Find the closest point to y in the subspace W spanned by vị and v2. 3 1 -2 y V2 13 3

A: To find  The closest point y in the subspace W spanned by v1 and v2.

Q: Determine whether the following are subspaces of R2×2: The set of all singular 2 × 2 matrices

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Q: let S be the collection of vector [x] (3x1 matrix) in R3 that satisfy the given…

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Q: Determine whether H is a subspace of M22. Give reasons! -X IX H={A€ M22 : A = 0 2x

A: Set of all 2*2 matrices denoted by M22 forms a vector space. We have to determine whether H is a…

Q: Give an example of a non-zero subspace of R^4 which has dimension > 1 and does not contain any of…

A: Consider the example f(x) = {2 + x + x2}, this given polynomial has dimension 3 with the basis {1,…

Q: can a subspace of R^n have a dimension less than n.

A: Yes , it can be .

Q: Explain why this statement is true: If V is a subspace of Rn, then there is a n×n matrix A such that…

A: To Proof :-  If V  is a subspace of Rn , then there is a n × n  matrix A such that V = Col A.

Q: Let vị 2,v2 8,and w Determine if w is in the subspace of R generated by v1 and v2.

A:

Q: 3. Let W be the subspace of R3 [x] spanned by the polynomials 1+2x+3x²+4x³, 2+3x+4x²+x³, 3+4x + x² +…

A: Please see the below picture for detailed solution.

Q: Prove that W1 = {(a,b) E R² : 4a – b= 0} is a subspace of R2.

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Q: Determine if W is a subspace of R³, and show why or why not

A: In this question, we have to check the given set is subspace or not

Q: Q3 shew that W2 = subspace of R2 is a

A: To show any subset of vector space is a subspace , prove the following condition : Set is closed…

Q: 3 Find a basis of the subspace of R' defined by the equation -7x1 – 5x2 – 4x3 = 0.

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Q: Prove that the set of mxn upper triangular matrices is a subspace of Mmxn(F).

A: We have to prove that -

Q: In R4 , find the dimension of the subspace spanned by the vectors {(1, 1, 1, 1)T , (1, 2, 2, 2)T ,…

A: Given vectors are {(1, 1, 1, 1)T , (1, 2, 2, 2)T , (1, 1, 2, 1)T , (2, 2, 3, 2)T , (4, 5, 6, 5)T }.

Q: at | f = a is a subspace of RI0,1] if and

A: Two step test

Q: 1. Determine whether W ER is a subspace of M. %3D b 2a

A: We have to determine whether W is a subspace of M22.   According top our guidelines we can solve…

Q: b.) show that IR³ - W₁ + W₂. t C.) Find a subspace V such that IR³ =W₁ U.

A:

Q: Verify that V5 is a subspace of RS

A: Please check step 2 for solution.!

Q: Show that W = {a + bx² € P₂|a, b = R} is a subspace of P2.

A: The solution is given as

Q: Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}

A: We want to show that  U∩W≠{0}

Q: 3 Find a basis of the subspace of R’ defined by the equation -5x1 – 7x2 – 2x3 = 0.

A: Consider the given equation:

Q: a b Show that W |a,b ER} is a subspace of M2x2. %3D -b a

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Q: Explain why the subset а — b S = a +b а,bER -26 – 3a of R3 is or is not a subspace of R³.

A: Given subset of R3 is  S={a-ba+b-2b-3a|a,b∈R} explain if S is subspace of R3

Q: In C[−π, π], find the dimension of the subspace spanned by 1, cos 2x, cos2 x.

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Q: determine the dimension of the subspace of R3 spanned by the given vectors.

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Q: Explain why the subset а —b S : a + b а,b€ R -2b — За of R³ is or is not a subspace of R³.

A:

Q: 3. Let W be the subspace of R3 [x] spanned by the polynomials 1+2x+3x²+4x³, 2+3x+4x²+x³, 3+ 4x + x²…

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

Q: Let W = {(" ):a = 2c = b = –3d} be a subspace of M22. Then dimension of W is equal to: None of the…

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Q: Determine whether W = {ao + a1x + a2x² + a3x°|ao + a2 = az ɑ1} is a subspace of P3.

A:

Q: -2 , find the closest point to v in the subspace W spanned by -2 Given v =

A: Introduction: Th formula for the projection of vector w on v is given by,…

Q: Let V = M22 and W = {invertible 2 x 2 matrices}. Determine whether W is a subspace of M2. %3D

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Q: Suppose that A is a fixed 2x2 matrix. Let U = {X ∈ M22 | AX = XA} Question: Prove that U is a…

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Q: Determine whether W is a subspace of V

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Q: Find the dimension of the subspace Hof R2 spanned by

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Q: Find the dimension of the subspace W of R4 spanned by S = {v1, v2, v3} = {(−1, 2, 5, 0), (3, 0, 1,…

A: Dimension of a subspace W is given by the number of linearly independent vectors in the basis of W,…

Q: Which of the following are subspaces of R°?

A: PART - A- Concept Used: W is said to be subspace of the vector space V if W≠∅…

Q: Investigate the dimension of the following subspace of R*. All vectors of the form (a,b,c,d), where…

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Q: Find a basis and the dimension of the subspace W = {(a+1)x+(2-b)x²; a,b e R} of P,.

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Q: Show that points on the plane x-2y+4z=0 form a subspace of R3

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Q: If A has the same four fundamental subspaces as B, does A = B?

A: Four Fundamental Subspaces: Let be a matrix of order and be its transpose matrix. Then The row…

Q: 2. Determine whether W is a subspace of V = C³ where W = {(0, b, c) E C3}

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Q: Find the closest point to y in the subspace W spanned by v1 and v2 2 1 y = -2 -3] 1 2 а) b) 2 c) 1…

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.