11. In the vector space R3 we are given the subspace Y =< (1, 1, –1), (0,-4, 5), (3,-1, 2) > . (a) Which conditions must the real numbers a, b and c satisfy in order the vector (a, b, c) lies in the subspace Y ? (b) Find a basis for Y. (c) Extend the basis you have found in (b) to a basis of the whole space R3.

Q: B = (1, x+1, x² + x) forms an ordered basis for P3. Give the B-coordinate vector of each of the…

A: The coordinate vector of v with respect to  is given by such that .(a) Given .Comparing the…

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

A:

Q: et B = · 9, (x − 1)², 3x³) be an ordered basis for P3. Find the coordinate vector of (x) = 3x³ + 2x²…

A: Coordinate vector

Q: Select all possible vector equations for the line through the points (1,1,1) and (3,4,5). OF (t) =…

A: Note that the vector equation of the line passing through two points a→ and b→is given by:…

Q: 3) Let S contain vectors of the form f(x) = a + bx + cx² + dx³ : f(-2) = 0 and f'(-4)= 0: Then a…

A:

Q: Find the terminal point Q of the vector v = 7i-j+3k given the initial point is P(-2, 3, 5) О (5, 2,…

A: In this question we have to find the terminal point of Q.

Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. 8-{8}-(-6) B…

A:

Q: 1 3 1 2 A=2 6 4 002 4 I= I Y Z ພ () and 6 = 3

A: Solution to the system

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

A: Given Data: Let us consider the given data, c 2,-2,1,0,2,-2,2,0,-1d 1,1,1,1,-1,-1,-1,1,-1,-1,-1,1…

Q: 3 2. (а) Do the vectors vị = -1 -1 form a basis for R³? , V3 = 1 > V2 = -I--- (b) Do the vectors vị…

A:

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A:

Q: Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² +…

A: We know that two vectors are linearly dependent if one vector can be written as a scalar multiple of…

Q: - Consider the following 3 vectors (1). 0 V1 V2 = 0 1 , V3 = 0 0 -1 Find a basis of span{v₁, v2, v3}…

A:

Q: 3. Suppose W (a) (b) a = = {( 2 ): 9₂ Prove that W is a subspace of M2x2 (R). : a, b, c ER CER}.…

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.