(1): All vectors of the form (a,0,0) that is S={(a,0,0):u = R} Show that the following sct is subspaces of (2): All polynomials a +ux +u,x +u,x' for which u, = 0 s-{peP:p-a +ax+a,x+a,r for which a, - 0}

Q: What is the matrix P = (P₁) for the projection of R³ onto the subspace V spanned by the vectors a₁ =…

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

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Q: Which of the following sets is a basis for the subspace U={(a,b,c,d)∈R4 ∣ a−b=0,a+d=0,b+d=0} in the…

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Q: 13 - Which one of the followings is NOT the subspace of R? ? =O W = {(a,2a): a e R} W = {(a, a + 1):…

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Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x²…

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Q: Let U C R’ be the subspace generated by (1, 1, 1, 0, 1), (2, 1, 0, 0, 1), and (0, 0, 1, 0,0). Let V…

A: The given problem is related with linear algebra. Given that U ⊂ ℝ5 is a subspace generated by 1, 1,…

Q: 5. Let W be the subspace of the vector space V = R spanned by the vectors =(1,3, 1, -2), B = (-3,…

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Q: {l: ol E M2x3: a = b = c = -3d } be a subspace of M2x3- Let W = d Then dimension of W is Оз 1 О4 O 2…

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Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

Q: Let u = (18,1,0). Find the orthogonal projection of u onto the subspace W spanned by the…

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Q: Let-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

A: We will use the one step test for vector subspace to check if W is a subspace or not. We know that…

Q: 1 5 0 2 4₂ -2, 1 Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the 1 1 0…

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Q: 3. Let W C R be an inner product subspace with standard dot product. { 12 then If W I1- 2r2 + 4 = I3…

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Q: 1 for which x value span the vector subspace? -1 13 - 2 -1 O A) 2 в) .1 O C) 0 D) 1 O E) -2

A: We have to find x

Q: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

Q: Let V be a vector space and W₁, W2 be subspaces of V. Then verify that W₁ + W₂ = {w₁ + W₂ : W₁ € W₁…

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Q: (a) Find orthonormal vectors 91, 92, 93 such that 91, 92 span the column space of 1 2 1 A - 1 -2 4…

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Q: Let U, W be subspaces of R" and assume UnW = {0„}. Prove that dim(U + W) = dim(U)+ dim(W). Here U +…

A: We have to prove given result:

Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

Q: Show that VI = (1,0,1) , v, = (1,1,0) , v3 = (1,1,1) span R'. Express vector v= (2, 1, 3) as linear…

A: v1 ,v2 ,v3 ,...,vn span R^n if det(v1,v2,...,vn) is non zero

Q: Verify that Rn is a vector space if R, be the set of all 1 x n matrices [a a2 an] ....

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

Q: Find a vector-valued function whose graph is the plane x+y+z= 12, O r(u, v)=-ui-vj+(12-u-v)k O r(u,…

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Q: Hello , I need help in Algebra a, 6, c E R. \ be Which of the following are subspaces of the R3 (a,…

A: Definition: The subset W of a vector space V is said to be a subspace if it satisfies following two…

Q: The set S = {(2a, b, a - b): a, b = R} quos & jonai (o) tails wol2 woled old is a subspace of R³.…

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Q: Vi and V2 be subspaces of R* (over R) Their intersection V=v,nV; is the set of all vectors that lie…

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Q: Let S = {[" e Mzxzi a = d and b + c = 0} be a subspace of M2x2- Then the dimension of S is equal to:…

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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.