Let W = {a + bx + cx2 + dx c- 3d = 0} be a subspace of Pg. Then th dimension of W is equal to %3D O None of these O 2 0 1 O 3 O 4

Q: Let W be the set of all 2 x 2 matrices A = |" 2 such that Az = 0, where z = H. Is W subspace of M22?…

A: Given that W is the set of all 2×2 matrices A such that Az=0 where A=abcd. Here z=11. We have to…

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

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

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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: 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 W of all 2x3 matrices of the form a I where c = a + b, is a la 0 subspace of M23. a. Find a…

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

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Q: b] Let W be the set of all 2 × 2 matrices A = such that Az = 0, where z = ||. Is W subspace of M22?…

A: A set W of vector space V over field F is said to be subspace of vector space V if W is itself a…

Q: Let W be the set of all 2 × 2 matrices A = " d. such that Az = 0, where z = |. Is W subspace of M22?…

A: Use the properties of a subspace or definition of subspace. Assume that the condition is true and…

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: Find a basis for the given subspace of R° , and state its dimension for the plane 4 x - 2 y + 5 z =…

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Q: Let W = {a + bx + cx² + dx°|c - 3d = 0} be a subspace of Pa. Then the dimension of W is equal to 3.…

A: PnF is set of all polynomials of degree nand smaller . PnF denotes the vector space over field F…

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: 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 S = ( (x.y, 2) ER |2 = 2, x,y,ZER)is a subspace under vector addition and scalar…

A: This question is related to linear algebra topic vector space.

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: Let V be a subspace of Rª spanned by Select one: O a. 2 O b. 1 O c. 3 d. 4 WN O 0 2 3 st -3 10 4 -6…

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Q: Let W = {( ):a :a + 2c = 0 and b-d = 0} be a subspace of M22. %3D %3D Then dimension of W is equal…

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Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 1 -1 1 -1 1 1 1 [1] 1 II…

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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

A: As given W be a subspace of P3.

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

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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: Consider the following subspaces of R3: U=span[(2, 1, 1), (1, 2, 0)] W=span[(0, 2, 1), (0, 1, 2)]…

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Q: Theorem 6.14. For any a < b in R, the subspace [a, b] is compact.

A: The objective is to prove that any a≤b in ℝ the subspace a,b is compact. Let's prove the theorem by…

Q: Let  S=span(e1),  T=span(e2) and  W=span(e1+e3) be subspaces of R3.  S is orthogonal to T, T is…

A: Orthogonal Subspace

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: Let W fa + bx + cx2 + dx'| a+ b 0 and c-3d 0 } be a subspace of Pg. %3D %3D %3D Then the dimension…

A: a+b=0  and c-3d=0 b=-a and c=3d Equation given is; a+ bx+ cx2+ dx3  = a- ax+ 3dx2+ dx3 that can be…

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…

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

A: dim(W) = number of vector in the basis of W.

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: Let W = {(" ):a = 2c = b = –3d} be a subspace of M22. Then dimension of W is equal to: None of the…

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Q: Let W = {(" ):a+ 2c = 0 andb-d 0} be a subspace of M22. %3D Then dimension of W is equal to: O 1…

A: The solution is given in the next step.

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 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: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

Q: 3) Show that the set of all elements of the form (x + 2y,x + 3z, 2x + y + z), where x, y, z E F, is…

A: We have, (x+2y , x+3z , 2x+y+z),where x, y, z € F.

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

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

A: Use the concept that dimension of subspace is number of free variables.

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: Let A be an mxn matrix. Prove that W = {x ER" | Ax = 0} is a subspace of R", where W is the solution…

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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: Let  S=span(e1),  T=span(e2) and  W=span(e1+e3) be subspaces of R3.  S is orthogonal to T, T is…

A: Given that S=spane1 and W=spane1+e3. To prove that S is orthogonal to W. Let x,0,0∈spane1 and…

Q: Show that W={(x1,x2,x3,x4) : x4-x3=x2-x1} is a subspace of R^4  spanned by vectors…

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

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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.