-3 6. -1 1 -71 6. Let B = 1 -2 3 -1. Determine a basis for, and dimension of, the following 2 -4 8 -4] subspaces: a. The column space B. b. The row space of B. The null space of B. с.

Q: 4: Let H1 and H2 be two subspaces of R". Show that H1 n H2 is also a subspace of R".

A: To show a set W to be a subspace of the of a space X if a,b∈W then a+b∈W   and for a scaler λ and…

Q: 5.- Demonstrate whether the vectors of the following vector space are linearly dependent or linearly…

A:

Q: a) {(1,-1,2),(5,-4,1),(7,-5,-4)}. b) {(1,3,3),(1,5,-1),(2,7,4),(1,4,1)}.

A: To Determine a basis for the subspace of Rn spanned by the given set of vectors by usingthe concept…

Q: Let V₁ 1 -2 3 2 {V1, V2,V3}. V₂ = 2 -2 V3 7 8 7 - 10 and u = Is u in the subspace of R4 generated by…

A:

Q: For the subspace below, find a basis 9a + 18b3c 3a-b-c -6a +5b+2c -3a+b+c a, b, c in R a. (9,3,…

A: This question is related to topic basis of vector space . Here we have to find basis of given…

Q: Let -2 4 -5 A 4 -3 Сл 5 -2 4 -5 A basis for the column space of A is { }. vector

A: A basis for the column space of matrix A is given by the set of columns corresponding to the pivot…

Q: if W is the subspace spanned for the 3 vectors, find the sets that serve as a basis for W choices:…

A: The given vectors: v1=-1-75  ,    v2=4-59 ,    v3=69-1

Q: Find the dimension of the following vector spaces. (a) V = {0}: dim V = (b) V = R¹: dim V- (c) V is…

A: (.) Dimension: The number of vectors in a basis of a vector space  is called dimension of..(.)…

Q: b) Then find the projection of b=(3,1,-3,4) onto the column space of 0 1 A 1 1 1 2

A:

Q: 20 n) Given below are subsets of different vector spaces. Determine whether or not each subset is a…

A:

Q: Let M3,3 denote the vector space of all 3 × 3 matrices. Let L3,3 denote the set of all lower…

A:

Q: Let A 1 3 = 0 3518 5 - 1 1 020 2 1 1 -2 0 8 - -2 3 Find a basis for the row space of A.

A:

Q: 3. Determine whether the set W = {(0,x2, 3, x4) : where x2 and x4 are real numbers} is a subspace of…

A: Subspace of a vector space

Q: 2а + b - Зс 4а — 2b + 5с (а) S %— E R* : a, b, c ER a а +b+c a X1 X2 (b) S = ER: 2x + х2 — 7хз + 8х4…

A:

Q: 4 11 5 -7 -97 0 1 4 11 5 -7 -97 6. is row equivalent to B= 5 -2 -4 2 4 3 3 3. If A= -1 1 find bases…

A: Given the matrix is A=4115-7-9-2-4246-107105-3-7028 which is equivalent to…

Q: Let -4 M = 3 be a vector in the vector space V of 2 × 2 matrices with real number entries. Let B be…

A: handwritten solutions attached.Explanation:Step 1:Step 2:

Q: -10 2 -+-+- = -3 8 ) Given : -5 B-B and -4 6 -34 find the closest point to in the subspace W spanned…

A:

Q: Find an explicit description of the null space of matrix A by listing vectors that span the null…

A:

Q: -6 -0-0-0-8 9 6 Let v₁ = -3 4 3 = 1. Is w in {V1, V2, V3}? Type "yes" or "no". 13 9 and w= 6 10 4.…

A:

Q: 2 Find bases and dimensions for the four subspaces associated with A and B: A = 1 2 4 and B= = 1 24…

A: We will find the bases and dimensions.

Q: Let V₁ = (1,4,5,6,9), v₂ =(3, 2, 1,4, -1), V3 = (-1,0,-1, -2, -1), V4=(2,3,5,7,8), Find a basis for…

A:

Q: Find a basis for the subspace of R* consisting of all vectors of the form (a, b, c, d) where c = a +…

A: To Find: Basis for the subspace of R2  of the form (a,b,c,d) such that c=a+7b and d=a-6b

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.