a) Determine whether S = {(1,0,-1), (2,1,0), (3,1,−1), (1,1,1)} spans R³. b) Find all c ER for which S = {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly independent set of vectors in R³ c) Determine whether W = {(x, y, z) € R³ | x² + y² = z²} is a subspace of R³

Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

A: (a), (b) , (c), (d)  are subspaces .

Q: Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span.…

A: a) Suppose that    be  a  basis  of      Then, which is  a  contradiction.    Hence, is  not 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: In linear algebra, if W is a subspace of R^4 whose dimension is 2 then any set of 2 vectors from W…

A: The given statement, "If  is a subspace of  whose dimension is  then any set of  vectors from  is a…

Q: Why is this set not a subspace of R^3? W = { (a1, a2, a3) : a22 = a1 - a3 } ( the two 2s are…

A:

Q: Wi = {(a,b,c,d) E R* : a+ b+ c = 0} ve W2 = = 0, b = 0}, Being subspaces of R^4 {(a,b,c,d) e Rª : a+…

A: For the given subspaces W1 and W2, we have to calculate…

Q: Which of the following sets is a basis for the subspace U={(a,b,c,d)∈R4 ∣ a−b=0,a+d=0,b+d=0} in the…

A:

Q: 13 - Which one of the followings is NOT the subspace of R? ? =O W = {(a,2a): a e R} W = {(a, a + 1):…

A:

Q: For any fixed vector v in R^n, the set V=?x∈R^n :v^(T)x=0 is a subspace of R . Assuming v does not…

A: According to the given information, Let V be a fixed vector in Rn, the set V is given as:

Q: Find a minimal spanning set for the subspace spanned by the set of vectors: S={, , , }

A: The given spanning set is S=1, 0, 0, -1, 4, 4, 0, 0. We have to find the minimal spanning set.

Q: (H) {| R uzayı 2)

A:

Q: Sui+ (v,u2)u2+ ··+ (v,uk)uk. =(v) is the closest vector to v in U and that it is the Iv - proja(v)I

A: To show, projαv is the closest vector to v in U and that it is unique such that, v-u≥v-projαv if…

Q: 2) One of the following subsets of IR2 is not subspace: a) S = {, xeR} b) s = {], = x3} %3D %3D e) s…

A:

Q: Prdlem 6.36 Pert B)

A: It is double Integral

Q: 3. Let S, and S, be two subspaces of R such that s, n s, = ((0,0,0,0,.0)) and dimension(S,) =…

A:

Q: {l: ol E M2x3: a = b = c = -3d } be a subspace of M2x3- Let W = d Then dimension of W is Оз 1 О4 O 2…

A:

Q: Let {v1 = (1,2,3,5,9), v2 = (3,1,2,8,9), v3 = (2, -5,5,9,4)} and {u1 = (0,1,1,1,2), u2 = (0,2, -2,…

A: The given question is related with vector space. Given that , v1 = 1,2,3,5,9 , v2 = 3,1,2,8,9 , v3 =…

Q: Let W = {[ W is not 2a 46 : a, b ER ». Determine whether W is a subspace of R³. a subspace of R³…

A:

Q: Suppose V is finite-dimensional and U and W are subspaces of V with W^0 ⊂ U^0. Prove that U ⊂ W.

A:

Q: Show there is no proper five dimensional subspace of R^5. (i.e. If V is a subspace of R^5 with dim…

A: To Show: If V is a subset of ℝ5, with dimV =5 then V=ℝ5.

Q: Let vl ་ མ། 2 - - ་ -2 and determine if w is in the subspace of R³ generated by v¹ and v². Show your…

A:

Q: W = (x:x= X1 X2 LX3 where x3 = 5x₁ + 8x2

A:

Q: Determine whether the given subset is subspace of R^3 W={(x1,x2,x3):x1+x2+x3=0}

A: Let the subset W is given as W={(x1,x2,x3)| x1+x2+x3=0} Determine whether the given subset is…

Q: Verify all vector space axioms under the given operations (x,y,z)+(x',y'z') = (x+x'+1,y+y'+2,z+z'+3)…

A: The objective of the question is to verify if the given operations satisfy all the axioms of a…

Q: Let (V,(*,*)) be an F-inner product space,where F is either R or C. LetU C V be a subspace and let a…

A:

Q: Let V be the subspace of R' spanned by vi = (1, 3, -2, 2, 3 ), v (1, 4, -3, 4, 2 ), v3 (1, 3, 0, 2,…

A:

Q: 3) Let W = { (x, y, z, t) : x = 0, y = -z } be subset of IR*. Is W a subspace of IR* ?

A:

Q: V {(x1 , X2, X3 ) E R³ |x2 + x3 = 3} %3D nin R3'ün bir alt uzayı olup olmadığını gösteriniz.

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.