Extend the linearly independentSet S={x+1, 2x²3 to the space base P₂ (R)و

We are given a linearly independent set S= {x+1, 2x2} We have to extend S to basis of P2(R). Let…

Answered: Extend the linearly independent Set…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

See similar textbooks

Similar questions

Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Find a basis for R2 that includes the vector (2,2).
Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.
Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are linearly dependent in the vector space C[0,1], but linearly independent in C[1,1].
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
,x43x-2 4. Determine whether the veltars X-I and X²-3x+2 dre linearly independent Or dependent in P2 (te vector Space of Polynomials of doyree less than equal to 2). or
. Let V be the set of all pairs (x,y) of real numbers together with the following operations: (x1,y1) (x2,y2) = (4x1 + x2 − 4, Y1 + 3 y2 − 3) c(x,y) = (cx- c+1, cy − c + 1). (a) Show that scalar multiplication distributes over vector addition, that is: c((x1,y1)(x2,y2)) = (c○ (x1,y1)) + (c○ (x2,y2)). (b) Explain why V nonetheless is not a vector space by showing that a vector space property does not hold for this set with these operations.
In the vector space P3(R), let S = {p1(x), P2(x), P3(x)}, where p1 (x) = 63x° + 19x² – 37x – 41, P2(x) = –189x – 57x² + 111x + 123, P3 (x) = 45x – 26x? – 55x + 92. (a) Determine whether S is linearly independent. (b) Determine whether (S) = P3(R). (c) Find the dimension of (S). 4.
Let 2 3 2 X = X2 = X3 = 6. 3 4 4 (a) Show that x1, X2, and x3 are linearly dependent. (b) Show that x¡ and x2 are linearly independent. (c) What is the dimension of Span(x1, X2, X3)?
Let T R² R² be the linear operator defined by 9x1 x2 T([22]) = [972] and let B = {u₁, u₂} be the basis for which u₁ Find [T]B. (??) |[T]B = |( 1 - [ 3 ] ₁ ₁₂ = [¹] ₁ 9

SEE MORE QUESTIONS

Recommended textbooks for you

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Extend the linearly independent Set S={x+1, 2X²} to the space base P₂ (R)