A) Find an ortho Connell basis  u1,u2,u3 for the sub space W=span { v1,v2,v3} such that all entries in each Vector u1 are integers B) WITHOUT using linear systems express the vector  x=4v1-3v2+2v3 € W as a linear combination of the vectors u1, u2, u3 found in part A

Q: Let S be the subset of R2 consisting of all vectors of the form (a, b + 3). a) Show that (5, 2),…

A:

Q: Find a basis for the solution space of the given homogeneous linear system. X4- 3x2 + 2x3 - 3x4 = 0…

A: To find a basis for the solution space of the given homogeneous system

Q: Let {v1, v2, ..., vn} be an orthogonal set in R" with respect to the Euclidean inner product. Let A…

A:

Q: Consider the system of vectors (1,2, 1, 1)", (0,1,3, 1)", (0,3,2,0)", (0,1,0,0)". a) Prove that it…

A:

Q: If P= (2, 7) and Q= (2, -3), which could be the coordinates of R if triangle PQR is isosceles?  I…

A:

Q: its) Let P3:= {ao+ a₁x + a2x² + a3x³|ao, a1, a2, a3 € R} be the vector space of polynomials of…

A:

Q: 2) Let u =(1,0,0), v = (0,1,0), and W is the set of all vectors (s,s,0) where s is any real number.…

A:

Q: Find the basis for the orthogonal complement V: v1=(1,-3,3,5) v2=(2,-5,9,3)

A: The given vectors  and .The objective is to find the orthogonal complement of the given vectors.

Q: Exhibit a basis for M2x2, the vector space of all 2 x 2 matrices of real numbers.

A:

Q: The vector w = and V3 = True False 1 -5 0 28 -31 8 31]" in M2x2 vector space is a linear combination…

A: Given that w=0828-31v1=1-210v2=-1308v3=1-4-53

Q: Compute the Binary distance between vectors [2, 1, 0] and [8, 5, 0].

A: Given vector points are (2, 1, 0) and (8, 5, 0)  Let (x1 , y1 , z1 ) = (2, 1, 0) And (x2 , y2 , z2 )…

Q: Suppose ₁, 2, 3 is an orthogonal set of vectors in R³. Let w be a vector in Span(V₁, V2, V3) such…

A: Given: v1, v2, v3 is an orthogonal set of vectors in ℝ5.           v1·v1=30, v2·v2=25.25, v3·v3=9…

Q: Show that if a vector space V has one basis of n distinct vectors, then every basis for V has n…

A:

Q: Let {u₁, U₂, U3, U4} be the orthogonal basis for R¹ given below. Write x as a sum of two vectors v₁…

A:

Q: 3) For each set of vectors below, determine if the set is dependent or in- dependent. If the set is…

A: We will first check the linearly independence of this set of three vectors

Q: A boy has a collection of 20 pennies, 8 nickels, 10 dimes and 15 quarters. How many coins must the…

A: ANSWER :

Q: Find a basis of Span((1,-1,3,0), (2, 1, -2, -1), (3, 3, -7,-2)).

A: We have to find a basis of Span ((1,-1,3, 0), (2, 1, -2, -1), (3, 3, -7,-2)).

Q: If {v1, V2, V3} is an orthogonal set of nonzero vectors in an inner product space V, then prov that…

A: This question is related to linear algebra (inner product space).

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.