Determine all values of k so that S= {k- kx2,3+ kx,2 + x + kx²} is a basis for P2, the vector space of polynomials of degree less than or equal to 2. O A. K# 1,2,4 O B. K#1 O C.K#0,1,2,- 3,4 O D. K# - 3,0,1 O E. K#0, – 3,4

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A: given B=1+x-2x2 , -1+x+x2 , 1-x+x2B'=1-3x+x2, 1-3x-2x2 , 1-2x+3x2 b) find the coordination matrices…

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Q: Which of the followings is a basis for P3: a) {x³,x², x³ + x²,x} b) {x³, x(x + 1), 1} c) {x3, x3…

A: OPTION (C)  IS  CORRECT.   Dimension of P3 is 3+1= 4 , so any linearly independent set of 4 vectors…

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A: Given:

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Q: T1. Find a basis for the column space of 2. 6. 8 4 12 3 9. -2 8 6. 18 6 A = | 3 9. -7 -2 -3 -1 2 6 5…

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A: The answer is:  (A) S is a basis of P2. Proved below.

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A: see below the answer and explanation

Q: 2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B {1+x – 2x2, –1 +x…

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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.