Problem 2. Cordylia is a being who exists within six spacial dimensions as opposed to the mere three in which humans beings live. She is a scientist who, in her flying saucer, travels between the moon of the solar system's third planet to the upper atmosphere of the planet itself in order to study the planet's flora and fauna. During her studies near the Catskill mountains she ended up being observed by a member of the planet's current dominant species and, as is protocol, she decides to abduct, study and tag this specimen who was able to properly observe her (after which she, again as protocol dictates, will erase its memories of the encounter and return it to the planet). Before pressing the activation rune in order to abduct the specimen with one of her manipulator arms, she hesitates and goes to check the calibration of her linear transporters. Cordylia often studies the two dimensional creatures living in the realm designated "Flatland" and, as the pesky stain on the carpet of her saucer is testament to, irreparable damage is done to specimens living in three dimensional space if her transporter attempts to map them into a two or one dimensional space. Cordylia has three linear transporters which allow her to bring three dimensional beings inside her six dimensional saucer; the linear maps the transporters operate by are given by the matrices 102 A = 101 013 -3 1 0 -1 0 -1 1 1 4 127 B 1 0 0 010 001 100 010 0 0 1/ ,C= 1 2 3 -1 -2 -3) D = -1 0 1 1 0 22 0 Then, to return the specimens back to three dimensional space, she has three more reverse transporters whose operations are given by the matrices 0 3-2 1 3 1 0 0 -4 2 1 3 3 -3/ 1 3 0 1 0 -1 1 4 1 1 1 150 0 0 -1 ,E= 0-2 -2 -2 100000 F=|0 1 0 0 0 0 0 0 1000 (a) In her past experiments, irreparable damage was done to her three dimensional specimens if any of their atoms were collapsed to one another by her transporters so, to ensure the safety of the specimen, she wishes to avoid such a collapse. Which of the transportation matrices A, B and C can be used to ensure that no collapse will occur when transporting a specimen into her saucer.

Problem 2. Cordylia is a being who exists within six spacial dimensions as opposed to the mere three in which humans beings live. She is a scientist who, in her flying saucer, travels between the moon of the solar system's third planet to the upper atmosphere of the planet itself in order to study the planet's flora and fauna. During her studies near the Catskill mountains she ended up being observed by a member of the planet's current dominant species and, as is protocol, she decides to abduct, study and tag this specimen who was able to properly observe her (after which she, again as protocol dictates, will erase its memories of the encounter and return it to the planet). Before pressing the activation rune in order to abduct the specimen with one of her manipulator arms, she hesitates and goes to check the calibration of her linear transporters. Cordylia often studies the two dimensional creatures living in the realm designated "Flatland" and, as the pesky stain on the carpet of her saucer is testament to, irreparable damage is done to specimens living in three dimensional space if her transporter attempts to map them into a two or one dimensional space. Cordylia has three linear transporters which allow her to bring three dimensional beings inside her six dimensional saucer; the linear maps the transporters operate by are given by the matrices 102 A = 101 013 -3 1 0 -1 0 -1 1 1 4 127 B 1 0 0 010 001 100 010 0 0 1/ ,C= 1 2 3 -1 -2 -3) D = -1 0 1 1 0 22 0 Then, to return the specimens back to three dimensional space, she has three more reverse transporters whose operations are given by the matrices 0 3-2 1 3 1 0 0 -4 2 1 3 3 -3/ 1 3 0 1 0 -1 1 4 1 1 1 150 0 0 -1 ,E= 0-2 -2 -2 100000 F=|0 1 0 0 0 0 0 0 1000 (a) In her past experiments, irreparable damage was done to her three dimensional specimens if any of their atoms were collapsed to one another by her transporters so, to ensure the safety of the specimen, she wishes to avoid such a collapse. Which of the transportation matrices A, B and C can be used to ensure that no collapse will occur when transporting a specimen into her saucer.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 14AEXP

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