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

Q: Let W = Span thogonal to W. -3 2 be a subspace of R4. Find W₁, the subspace

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Q: 2. Let а — lb +c а S = {[a – b ,b,c € R a a. Show that S is a subspace of M2x2. 31 -2 31 5 b. Is |…

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Q: III. SUBSPACES 2. Which of the following subsets of R* are subspaces of R¹? b. W={(a,b,c,d)|…

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Q: Let H = {[ 21 12 x1, x2 € R 1,2 Show whether or not H is a subspace of R3.

A: We satisfy the clouser and scaler multiplication and show that 0 vector is also in H so H is a…

Q: а. W- : x is a scalar |2x + y b. W = : x, y are scalars x + y c. W = +1 : x is a scalar

A: we have to check subspace.

Q: Let y = - 11 - 1 1 9 1 0 - 1 2 , and V₂ = -6 1 . Find the distance from y to the subspace W of R4…

A: y =

Q: For a basis for the following subspace of R4:

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Q: If S is a subspace of R", then so is the orthogonal complement of S.

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Q: 1. Determine if each of the following is a subspace of R³ All vectors of the form (a, 0, 0). All…

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Q: Determine whether W is a subspace of V

A: Given: V=M22, W=abcd : ad≥bc. To check: Whether W is a subspace of V or not.

Q: 3. Suppose that u and vare nonzero vectors and that S is a subspace. Prove that if u ES and v E St,…

A: Let u and v be non-zero vectors and S be a subspace. Assume that u∈S and v∈S⊥. This means that…

Q: Suppose thatT: V + Wis a linear transformation then .is subspace of the domain V .a The range .b the…

A: Suppose T :V to W is a linear transformation then the kernal is a subspace of the domain V

Q: . Let L ⊂ R3 be the following subspace: L = {(x1, x2, x3) : x1 + x2 + 3x3 = 0}, and let ℓ be the…

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Q: Given = 5 # -6 find the closest point to in the subspace W spanned by 3 2 6 and 0 -6 -7 -54

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Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace a. Find a nonzero…

A: W=span

Q: 1 . Determine which of the following subspaces of R³ are identical: U₁ = span[(1, 1, -1), (2,3,-1),…

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Q: S = {[a _b c]€R³|c = ab} _is a subspace of R3. صواب İhi

A: We have to solve given problem:

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: S= {[a b c]e R³|b= 3a and c = a +3} is a subspace of R' %3D ylgn O ihi O

A: To check whether S=a b c∈ℝ3|b=3a and c=a+3 is a subspace of ℝ3

Q: 4. Consider the following subspaces of P. H = Span{1+t, 1 –} and G Span{1+t + , t-, 1+t+*} Find dim…

A: According to the given information. Consider the subspaces of P as:

Q: Let S be a 2D subspace of R. Find projs if projs =

A: Let S is a 2D subspace of ℝ3 projs<2,-1,1>=<0.5,0.5,1> So consider the 2-D plane given…

Q: Find bases for the following subspaces of F5: and W₁ = {(a1, 02, 03, 04, 05) € F5: α₁ - 03 - α4 = 0}…

A: Given subspaces areWe have to find the bases for the above subspaces also we have to determine their…

Q: 4. Consider the following subspaces of P. H = Span{1+t, 1– t°} and G=Span{1+t+t°, t – t°, 1+ t+t®}…

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Q: If W is a subspace, then ||projwv||² + ||v – projwv||2 = ||v|?.

A: Given W is a subspace of a vector space V. Now projWv denotes the projection of vector v onto the…

Q: Find all values of h such that vector y will be in the subspace of R spanned by vectors 3. V1, V2,…

A: we will first find the equivalent matrix and then reduce it to row echelon form

Q: Consider the following subspaces of P. H = Span{1 +t ,  1 - t3} and G = Span{1 + t + t2,  t - t3,  1…

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Q: Recall that lines through the origin are subspaces of R². 2x and W₂ is the line y = If W₁ is the…

A: Given, W1 is the line y=2x and W2 is the line y=-3x ,we have to find which statements are true about…

Q: If V is a subspace of M5x5 (R) such that dim(V) = 2, what is dim(V+)? 07 10 3 23

A: Given that  is a subspace of  such that .The aim is to find .

Q: Which of the following subsets of R* are subspaces of R*? b. W = {(a,b,c,d)| c=a+2b, d=a-3b}

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Q: Let A = {(1, –2,0), (0,0, 1), (-1, 2,0)}. Determine if A spans R. If A does not span R°, give a…

A: To find wheather A spans R3 we have to check if it forms a basis in R3