Let W = {a + bx + cx2 + dx³| a + b = 0 and c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to %3D 3. None of these 4.

Q: Let W = {a + bx+ cx² + dx³| a + b = 0,c – a = 0, and d – 3a = 0} be a subspace of Pg. Then the…

A: We have to find

Q: Let S E M2x2; a = d and b +c = 0} be a subspace of Max2. %3D Then the dimension of S is equal to: O…

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Q: Let W - (a + bx + cx + dx'l a +b-0 and c - 3d = 0) be a subspace of Py. Then the dimension of W is…

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Q: The dimension of the subspace W = {A E R™Xn: A is diagonal} is 2. balg j

A: Dimension of the subspace:          If V is spanned by a finite set , then V is said to be finite…

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: Determine whether the following are subspaces of R2×2: The set of all singular 2 × 2 matrices

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Q: Let AX = B be a nonhomogencous system of linear equations in n unknowns; that is, B+ 0. Show that…

A: Let us denote the solution space by W So, W = { X in Kn : AX = B } which is a subset of Kn

Q: Let W = {a + bx + cx² + dx³| a + b = 0,c – a = 0, and d – 3a = 0 } be a subspace of P3. Then the…

A: dimW = 1

Q: Suppose that A is an n x m matrix of rank 3, the nullity of A is 3, and the column space of A is a…

A: Answer (6)  Suppose that A is an n × m matrix of rank 3 , the nullity of A is 3 , and the column…

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: Determine whether the following are subspaces of R2×2: The set of all 2 × 2 lower triangular…

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Q: Find a basis for the subspace а : a, b, c, d E R with 3a + b=0 and c+ d = 0 C W = 6. 6. d of R4.

A: Since 3a+b=0 Therefore b= -3a  And since  c+d=0  Therefore d= -c

Q: 1. Suppose that A is an nxn non-zero, real matrix and 2 is a fixed real number. Let E ={x=R* : AT =…

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Q: 3. Let W be the subspace of R3 [x] spanned by the polynomials 1+2x+3x²+4x³, 2+3x+4x²+x³, 3+4x + x² +…

A: Please see the below picture for detailed solution.

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

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Q: Let W = {a + bx + cx² + dx³[c – 3d = 0 }) be a subspace of P3. Then the dimension of W is equal to O…

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Q: The set of all 3 x 3 matrices of the form 0 0 0 0 0 -5x 0 0 0 where x is a real number, is a…

A: Given :M=00000000-5x

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

A: We have to choose the correct answer from the given options

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

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Q: What is the dimension of the following subspace U of R2x2 ? 3 U = span({ }) -2 -2

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Q: Let W {a + bx + cx2 + dx³| a + b = 0 and c - 3d = 0} be a subspace of P3. %3D Then the dimension of…

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Q: 2) Find all the invariant subspaces of the following matrix 0. 1 0 1 1 1

A: Given matrix is, Let, A=010010111 Now, calculating the eigen value of the given matrix.…

Q: A base of the subspace W={ (a, b, c); a-2b+c=0} is:

A: According to the question,

Q: Let W = :a +5c = 0} be a subspace of M22. %3D Then dimension of W is equal to: None of the mentioned…

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Q: If W is a 2 x 2 matrices A with trace equal to zero is a subspace of M2,2. Prove that span X = W.…

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Q: Let W be the set of all 3 x 3 matrices whose trace is zero. Show that S is a subspace of M33.

A: Let W be the set of all 3×3 matrices whose trace is zero. Show that W is a subspace of M33.

Q: Let W = {a + bx + cx2 + dx'|c-3d = 0} be a subspace of P, Then the dimension of W is equal to %3D 4.…

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Q: Let W = (a+ bx + cx² + dx*| a +b= 0,c-a = 0, and d-3a = 0) be a subspace of P. Then the dimension of…

A: The dimension of the vector space of polynomials in x with real coefficients having degree at most .

Q: What is the dimension of w = {A € M2x2 (R) : A"| =ö} ĄT -2 1 2 This is not a subspace

A: W=AEM2×2(R) : AT1-2=→0  Let A=abcd, a,b,c,dER     AT=acbd     AT1-2=→0  ⇒acbd 1-2 =00 ⇒a-2cb-2d=00…

Q: The set of all 3 x 3 matrices of the form 1 0 0 1 Lo o 0 0 Select one: True O False + 13x3 where a…

A: Answer: The solution is as given below:

Q: Let W = {a + bx + cx2 + dx'| a + b = 0,c- a = 0, and d-3a = 0 } be a subspace of P. Then the…

A: 1 is the answer.

Q: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

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Q: 3. Let W be the subspace of R3 [x] spanned by the polynomials 1+2x+3x²+4x³, 2+3x+4x²+x³, 3+ 4x + x²…

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

Q: Show that S = {(a,0, b)"|a,b E R} forms a subspace of R³.

A: The solution are next step

Q: Suppose W is a set of 2 x 2 matrices A with trace A = 0 , and is a subspace of M2,2 Consider the…

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Q: Let W be the subspace of M10,10 (i.e., 10 × 10 matrices) consisting of all matrices whose diagonal…

A: A basis B for a vector space V is a linearly independent subset of V that generates V.  The number…

Q: Let A be a fixed 10 x 10 matrix and let H be the set of all 10 x 10 matrices N with the property…

A: Given that A is fixed 10×10 matrix and H=N  NTA=AN. To find : H is a subspace of all  10×10 matrix…

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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Q: let W = {x €R3 , 1 such that Ax 2 where A is any 2×3 matrix is a subspace of R³ Select one: True…

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Q: Let S = {" E M2xzi a = d and b+c 0 be a subspace of M2x2. %3D Then the dimension of S is equal to: 4…

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Q: 6. a. Give a basis for the orthogonal complement of the subspace V C R' given by V = {x € R* : xị…

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Q: Consider the subspaces U = span{[3 -3 1],[12 3 -7]} and W = span{[-3 2 0],[1 8 -6]} of V = R1x3.…

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Q: Consider the subspaces U = span{[3 5 0],[0 12 -6]} and W = span{[–3 2 -1],[-15 7 -11]} of V = RIX3.…

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

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Q: Consider the subspaces U = span{[3 -4 -2],[6 -8 2]} and W = span{[ -2 -2 3],[2 -12 14]} of V = R'x3…

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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 w

A: Topic:- matrix

Q: Let W = {a + bx + cx2 + dx³| a +b = 0,c - a = 0, and d - 3a = 0} be a subspace of P3. Then the…

A: We have to check

Q: Let A e Mnxn and W be the set of all solutions for the homogenous linear system AX = 0. Prove or…

A: Given, A∈Mn×n and W be the set of all solutions for the homogenous linear system AX=0. We have to…

Q: Find the closest point to y in the subspace W spanned by v1 and v2 2 1 y = -2 -3] 1 2 а) b) 2 c) 1…

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Q: 49. Let A be a fixed n x n matrix and let S = {B e Mnxn | AB = BA} %3D Is S a subspace? Explain.

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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.