4. Consider the following subspaces of P. H = Span{1+t, 1-t3 } and G = Span{1+t+t 2, t – t 3, 1+t+t 3} Find dim H, dim G and dim H intersection G.

Q: 1. Consider the following subspaces of R³: U = {(x,x,y): x,y ER} and W = {(x,-x, 2x): x, y ≤ R} (a)…

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

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Q: Consider the following subspaces of P. H = Span{1 + t, 1 − t 3 } and G = Span{1 + t + t 2 , t − t 3…

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

A: Solution:-

Q: 2. Determine whether the set W = {(x,y, z)|x + y +z = 0} is a subspace of R3

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Q: Determine whether the following are subspaces of C[−1, 1]: The set of continuous nondecreasing…

A: According to the given information,

Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw (v) |||| 6 V H 14 2 and…

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Q: 4: Let H1 and H2 be two subspaces of R". Show that H1 n H2 is also a subspace of R".

A: To show a set W to be a subspace of the of a space X if a,b∈W then a+b∈W   and for a scaler λ and…

Q: Suppose V is an inner product space with dim V = 7 and U is a subspace of V with dimU = 2. Then dim…

A: We know that  The sum of the Dimensions of a subspace and the dimensions of its orthogonal…

Q: 2.14. Prove that two subspaces V1 and V2 are linearly independent if and only if Vịn V2 = {0}.

A: V1 and V2 are two subspace.

Q: Let W be the subspace of P3 spanned by {t³ +t² – 2t + 1, t² + 1, t³ – 2t, 2t³ + 3t² – 4t + 3}. Find…

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

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Q: Determine is Question 2 whether W = W = {(a; z { (a; 2; 6) | α; 6ER} subspace of R

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Q: 1. Determine whether w - {[:]•r:a-4-0} X1 E R? : : x1 – 23 = X2 is a subspace of R?.

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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: Which of the following sets is NOT subspace of IR? 2 Span -5 {8} Г1 2 31 The set of solutions to the…

A: solve the following

Q: [M] Show that w is in the subspace of R4 spanned by V1, V2, V3, Where 9. -4 -7 -4 -4 3 V3 = V2 = -4…

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Q: Let W1 and W2 be subspaces of a finite-dimensional vector space V. Determine necessary and…

A: Consider W1 and W2 be the subspaces of finite dimensional vector spaces V.

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: 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: 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: 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: Suppose that X = ER' :z + y + z = 0 and ² + y² = z² Determine (with justification) whether X is a…

A: Given  X=xyz∈ℝ3:x+y+z=0 and x2+y2=z2

Q: Let S1 = {(xy)/ x22y-1}, S2 = {(x,y)/x <3, 1s y 5} and S3 = {(x,y)/ O< x<3, 1sys5}. %3D Then: S1 and…

A: We use the result  compact subset of R is closed and bounded.

Q: Find the orthogonal projection of -5 -1 16 onto the subspace W of IR³ spanned by 4 -4 and 2 24 projw…

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Q: If Sz is a subspace of R* of dimension 3, then there cannot exist a subspace S2 of R* such that S, c…

A: S1, S2 are subspaces of R4 such that S1⊂S2⊂R4 with S1≠S2 and S2≠R4.

Q: 2) Let W1, W2 be subspaces of V. Prove that W1 UW2 is a subspace if and only if W1 C W2 or W2 C W1.

A: Let W1,W2 be subspaces of V. To prove W1∪W2 is a subspace if and only if W1⊆W2 or W2⊆W1

Q: Determine whether the set of all 3-tuples of the form (x, y, z), where z = x – 2y, form a subspace…

A: If W is a subset of a vector space V over a field F, then W is a subspace of V, only if it satisfies…

Q: If y is in a subspace W, then y - ŷ is not zero. Select one: O True O False

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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: Suppose that X = eR' : 2 + y + z = 0 and r²+y² = z² } . Determine (with justification) whether X is…

A: We have to check whether the set X is a subspace of the vector space ℝ3. We have to give a…

Q: 2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1,…

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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: 4) Find all values of h such that Y will be in the subspace of 3. R spanned by VI) V2, V3 if V I V2…

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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: 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: Let vi # v2 E R" and define W1 Span{v2}. Use the definition to show W+n W, is a subspace of R".…

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Q: 14) Find all values of h such that y will be in the subspace of 3 spanned by v1, v2, v3 if vị = 2,…

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Q: 5. Consider the vector space P2(R), the set of all polynomial func- tions of degree less than or…

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Q: 5. Let S = {x + 1,x2 – 2, x – 1,3}. Find a basis for the subspace W that is spanned by S.

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Q: 1- Show whether the set of polynomials a, +at +at+at ,where a, =a, +a, is a subspace of P3 or not ?

A: Let V be a vector space over the field F. A non-empty subset S of the vector space V is said to be a…

Q: Let WC R4 be a subspace such that W = span(w₁, W2, W3, W4), where 4 1 2 0 W1 = 1 0 1 0 9 W2 = 2 3 1…

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Q: 1. Decide if the following subsets W C V are vector subspaces or not (justify) (a) W = x €RCR?. COs…

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Q: 4. (a) Find a basis for the subspace H of R spanned by the following vectors: 00000 1 (b) What is…

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Q: If y is not in a subspace W, then y - ŷ is zeo. Select one: True False

A: If y is in subspace W, then the orthogonal projection of y onto W (y') is y itself.  And in that…

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

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Q: (5) Suppose that T E L(V) is such that all subspaces of V of dimension dim(V) – 1 are T-invariant.…

A: Please check step 2 for the solution.!

Q: Let W be a 3- dimensional subspace of R*, then Dim ( WnW) = Оз O 1 O None of these

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

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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.