Consider N column vectors in RN where the ith element of the ith column vector is:(1 if i = j(0, if i + j(a) Calculate:Show all necessary calculations.(b) Calculate:el =B =C =NΣ(ei)'eij=1N(el)'el-1j=2NŽª(c) Let A be an N X N matrix. Denote the {i, j}th element of A by aj. Calculate and describe the resultingvector/matrix:(ei)'A(ei)'Aek(ei)'AAek

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Consider N column vectors in RN where the ith element of the j¹ column vector is: e = {0,ifi #j = j a) Calculate: Show all necessary calculations. (b) Calculate: B = [(el)'ej j=1 N C = [(el)'et-1 j=2 (e¹) |

Consider N column vectors in RN where the ith element of the j¹ column vector is: e = {0,ifi #j = j a) Calculate: Show all necessary calculations. (b) Calculate: B = [(el)'ej j=1 N C = [(el)'et-1 j=2 (e¹) |

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 17E

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Question

Consider N column vectors in RN where the ith element of the ith column vector is:
(1 if i = j
(0, if i + j
(a) Calculate:
Show all necessary calculations.
(b) Calculate:
el =
B =
C =
N
Σ(ei)'ei
j=1
N
(el)'el-1
j=2
N
Žª
(c) Let A be an N X N matrix. Denote the {i, j}th element of A by aj. Calculate and describe the resulting
vector/matrix:
(ei)'A
(ei)'Aek
(ei)'AAek

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