18. Which of the following subsets S is a subspace of R²? (a) S= {(x1,x2)||#1| = |r2|} (b) S = {(x1,72)|r2 = #1 + 1} (c) S = {(r1,X2) | #2*1 = 0} (d) S%3D {(zn,zz) |피3D } %3D (e) None of the above

Q: 3. Let S be the subset of Mmn containing all matrices A such that (A)₁1 = 0. Determine whether or…

A:

Q: -4 Find the orthogonal projection ŷ of y = 4 onto the subspace 3 -3 W = Span { uj U2 = 2 Ex: 1.23

A: With the help of definition of projection of a vector on a subspace, we solve this problem.

Q: Which of the following is not a subspace of R? Select one: O A. W={X: I1 B W= {X:1= T, of I, = O…

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Q: Find the intersection of the following two affine subspaces of R4. 1 1 0 1 1 1 1 1 0 0 1 y 1 1

A: Let's find.

Q: QUESTION 6 and b= Let W=span ( - 1+x,1+x²) be the subspace of P₂ equipped with the evaluation inner…

A: let W=span-1+x , 1+x2 be the subspace of P2 if p=12+6x-12x2 then projwp=a+bx+cx2 find the value of a…

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

A: Let us apply elementary row operations on the given Matrix A to reduce it in reduced row Echelon…

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: 22.13 Suppose A =|1 2 and b=0 3 Compute x = (ATA)-'A*b, P= A(ATA)-A", and Ax Pb. What is the…

A:

Q: 3. Let S be the subset of Mmn containing all matrices A such that (A)11 = 0. Determine whether or…

A: Introduction: A subspace is first of all a non-empty subset of a vector space. If it is a vector…

Q: Let S = E M2x2; a = d and b +c = 0} be a subspace of M2x2- Then the dimension of S is equal to: 1 4

A: S=abcd∈M2×2; a=d and b+c=0 be a subspace of M2×2

Q: 5.7.5 ND Suppose that V has an inner product, and that n is in V. Show that the set Vo of all…

A: We will use the definition to prove that, V0 is a subspace of V, keeping in mind the properties of…

Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

A:

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: 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: Find a basis for the subspace of R3 spanned by S.S = {(1, 2, 4), (−1, 3, 4), (2, 3, 1)}

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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: Find a basis for the subspace of R3 spanned by S.S = {(4, 4, 8), (1, 1, 2), (1, 1, 1)}

A:

Q: 4. Suppose A is 5 x 7, and Nul A has dimens (a) What is rank A? Explain how you de= your answer. (b)…

A: Given, A is 5×7, and Nul A has dimension 5.

Q: If V is a linear subspace of R", and x1 , ×2 , ... , Xn E V, then we must have span {x1, X2, Xn} =V.…

A: To determine that the statement, if V is a linear subspace of ℝn and x1, x2,....,xn∈V, then spanx1,…

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

A:

Q: 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…

A:

Q: 3 1 Show that the null space of A is a 02 subspace of R³. Which subspace can you obtain by the…

A: It is given that,  A = 13-1024 We have to show that the null space of A is a subspace of ℝ3 and to…

Q: Show that H= {p € P3: p(0)+p(1) = 0} is a subspace of P3. %3D

A:

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

A: Two step test

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: Which of the following must be true? The set of all n x matrices having trace equal to zero is a…

A:

Q: 3.12. Show that for a subspace E we have (E-)- = E. Hint: It is easy to see that E is orthogonal to…

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Q: Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2,…

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Q: 4 6' Let S be the subspace of R° spanned by the vectors and and let b = 3 Find the point in 4 S that…

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Q: 2. The subspace in R3 is a plane whose equation is x+y+z=0 x-2=0 x-2y+z=0 (a) (b) 2-0 (c) y-2--0…

A:

Q: Find a basis for the subspace of R3 spanned by S. S = {(5, 9, 9), (1, 2, 2), (1, 1, 1)}

A: To find the basis for the subspace of R3 spanned by the given set of vectors S.

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

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

Q: Let W = {a + bx + cx? + dx³|c – 3d = 0} be a subspace of P3. Then the dimension of W is equal to…

A:

Q: -3 Find the orthogonal projection ŷ of y = -1 onto the subspace -2 5 W = Span { u1 = -5 u2 = -3 Ex:…

A:

Q: Suppose that S1 and S, are nonzero subspaces, with S, contained inside S2, and suppose that dim(S2)…

A: Dimension of the vector space is the number of vector in the basis. Basis : The set of vector that…

Q: Find a basis for the subspace of R3 spanned by S. S = {(1, 3, 6), (-1, 4, 6), (2, 4, 1)} EEE

A: Basis of subspace of ℝ3 i) It must be linearly independent. ii) Its span ℝ3

Q: Find a basis and the dimension of the subspace W of P3= {ax3+ bx2 + cx + d} defined by W = {PEP3:…

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Q: Which of the following sets are subspaces of R3: W1 = {(x1, x2, x3): x3 = 2x1 – 4.x2}; W2 = {(x1,…

A: A set W, is a subspace of a vector space ℝn if it satisfies the following three properties.  0 is…

Q: Which of the following subsets of R3x3 are subspaces of Rx3? OA. The diagonal 3 x 3 matrices OB. The…

A:

Q: 2. The set P3 of all polynomials of degree ≤ 3 with normal polynomial operations is a vector space.…

A: Check which of the following are subspaces of P3.

Q: 2. Determine whether the following subset S of R3 is a subspace or not. a) S = X2||x1x2x3 = X3 S.…

A: Let V be a vector space over field F. Let W be a subset of V then W is subspace of V over field F if…

Q: Find the orthogonal projection of -13] 15 onto the subspace W of R4 spanned by 4 and 5 -2 -2…

A:

Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12

A: To find  The closest point to V in the subspace spaneed by the given vectors.

Q: Show {s,t,4s-3t)|s and t are in ℝ} is a subspace of ℝ3

A: Let A= {s,t,4s-3t)|s and t are in ℝ}To show A is vector space it is enough to show that   v1,v2…

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: 10 - What is the dimension of the subspace below? w = sp {C J. C 9 C 3 a) O 2 b) O 0 1 d) O -1 e) 3.

A: According to question  We have to calculate the dimension of the subspace.

Q: 2 Find the dimension of the subspace H of R spanned by – 12 8 ..... dim H =

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Q: 4. The set W of polynomials of the form ao + a₁x + a₂x² + a3x³ + a4x¹, where ao = a₂ and a₁ = az…

A:

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

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.