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 S2 are compact subspaces of R.

Q: 1. The linear span of a set S is the (a) largest subspace contained in S. (c) smallest subspace…

A: # As per the guidelines we are entitled to solve one question at a time please resubmit the other…

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

A:

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

A:

Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: 2.3. For each of the following functions give a subset D of Y (possibly Y itself) on which the…

A: From the question post, it is clear that after finding D, you want us to check if it is actually a…

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

A:

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

A:

Q: 3. State why W = {x = (x1, 2, X3, T4) E R' : a1 + x2 + x3 + a4 < 1} is not a subspace of R. (H.W)

A:

Q: The subspace of R spanned by the vectors ui = plane passing through the origin. Express w = where wi…

A: Let W be subspace of ℝ3 spanned by the vectors u1=45,0,-35 and u2=0,1,0. Let A=x,y,z be a non zero…

Q: Decide if the following subsets are: {(x,y,z) e R³: 2x + y - 3z = 1}. {(x, y, z) e R³: 2x = y + z}.…

A:

Q: (b) For subspaces X and Y, the sum X + Y is a direct sum (denoted X + Y) if every VEX + Y can be…

A:

Q: Determine whether S={a, +a,x+a,x :a, +a, +a, = 0} is a subspace of P.

A: Here S is a subspace of P2

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

A:

Q: 4 1 Let V= { X= (X₁₂X²)X₁9X4) ER" : X₁ = a X₁ +bx++exs} Where as boc, are fixed real number show…

A:

Q: 4. Consider the ordered basis E = (₁.e₁-es) for R². If [v] = (1,-1)", then v= e, 4 c H (b) 2e +ez…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Determine the kernel and the range of the linear operator on L(x) = (x1 + x3, X2, 0)

A:

Q: 5. The solution set of the system Ax 0 with three unknowns is a subspace of the vector space M33 O…

A:

Q: True or False. Justify your answer. Let U Span{1+x, x+x²} and W = Span{x²} be subspaces of P2 (R).…

A:

Q: Show that yn for all n=1, 2₁- ✓

A:

Q: -(80) (b) 2. The subspace (a) x+y+z= By in R³ is a plane whose equation is x-2=0 (c) y x-2y+z=0 (d)…

A: Here i am using linear combination and then we saw the relation between the coordinates.

Q: (3) Is Mmxn(Q) is a vector subspace of Mmxn (R) over R?

A:

Q: Let S € R² | xy ≥ 0 Y where S uses the usual definitions for vector addition and scalar…

A: Given subset of is the following :Obviously Here noted that vector addition rule : and scalar…

Q: 3) Explain why S, = {(x, y) E R²:y > 0} and S1 = {(x, x²): x E R} are not subspaces of R?. %3D

A: We will solve both these parts using only basic knowledge of subspaces and vector spaces (in clear…

Q: 0 Find the orthogonal projection of 0 onto the subspace of R4 spanned by 121 2 and 20

A: To find the orthogonal projection of the vector onto subspace first check the subspace spanned by…

Q: 1. The linear span of a set S is the (a) largest subspace contained in S. (c) smallest subspace…

A:

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

A:

Q: Let V = R? and K = R. Which of the following are subspaces of V? Give reasons for your answers.…

A:

Q: U = {(z,w) ≤ C² : z²+u²=0}, W={(z,w) ≤ C² : Re(z) = Re(w)} Are subspaces of C²?

A:

Q: 1

A:

Q: Let S1 = {(xy)/ x22y-1), S2 = {(x.y)/ x $3, 15 y 5} and S3 = {(x.y)/ O< x<3, 15ys5}. Then: O s1 and…

A:

Q: Find the orthogonal projection of x³ € P3 onto the subspace Span (1, 1 + x, 1 + x²). Justify your…

A: Here we have given a vector space of  onto the subspace…

Q: Q3. Point a base of this subspace of R*: W = { (x,y,z,t) ||-y+z=0,t - = 0 }

A:

Q: C. TRUE or FALSE The vector 2 and 3 form a subspace in R3. Justify your answer.

A: Given vectors are &lt;1,1,1&gt;,&lt;1,2,1&gt; and &lt;2,3,2&gt;. We check whether this forms 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.