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1) Find the inverse of 6- 5V7 in the fied QI V7I a BEC ala + 6)= Àg + 2e %3D

1) Find the inverse of 6- 5V7 in the fied QI V7I a BEC ala + 6)= Àg + 2e %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3) Find the solution in the field of the complex numbers to the linear equation 1) Find the inverse of 6- 5/7 in the field Q[ V7 2) Show that for all 2, a, B E C, 1(a +B)3Aa+2R 2 Find the solution in the field of the compiex numbers to the linear equation 5) Let Fg have elements {0, 1, 2, 3, 4} and assume that addition and multiplication are given %3D 2x- (1+2i) = -ix + (2 + 2i). 2-i 1+2i/ bove elements (0, 1, 2, 3, 4} and assume that addition and multiplication are given 6+i %3D 4) Find all vectors v E C such that (1 + i)v+ 3+6i by the following tables: O5 01 234 O5 1 2 34 1234 0123 4 2. 2 4 13 1 1234 0 3. 3 142 2340| 1 43 21 3. 3401 2 4 4 01 2 3 a) How can we immediately tell from these tables that the operations of addition and multiplication are commutative? YOw and colums eueelo the ud. squc b) How can we conclude from the addition table that 0 is an additive identity? c) How can we conclude from the addition table that every element has an additive inverse relative to 0? d) How can we conclude from the multiplication table that 1 is a multiplicative identity? e) How can we conclude from the multiplication table that every non-zero element has an multiplicative inverse relative to 1? 6) Making use of the tables for the field Fs in exercise 5, find the solution to the linear equation 3x +2 = 4, where the coefficients of this equation are considered to be elements of Fg. GONES 7) Find all vectors v in F such that 2v + () 2.
Transcribed Image Text:3) Find the solution in the field of the complex numbers to the linear equation 1) Find the inverse of 6- 5/7 in the field Q[ V7 2) Show that for all 2, a, B E C, 1(a +B)3Aa+2R 2 Find the solution in the field of the compiex numbers to the linear equation 5) Let Fg have elements {0, 1, 2, 3, 4} and assume that addition and multiplication are given %3D 2x- (1+2i) = -ix + (2 + 2i). 2-i 1+2i/ bove elements (0, 1, 2, 3, 4} and assume that addition and multiplication are given 6+i %3D 4) Find all vectors v E C such that (1 + i)v+ 3+6i by the following tables: O5 01 234 O5 1 2 34 1234 0123 4 2. 2 4 13 1 1234 0 3. 3 142 2340| 1 43 21 3. 3401 2 4 4 01 2 3 a) How can we immediately tell from these tables that the operations of addition and multiplication are commutative? YOw and colums eueelo the ud. squc b) How can we conclude from the addition table that 0 is an additive identity? c) How can we conclude from the addition table that every element has an additive inverse relative to 0? d) How can we conclude from the multiplication table that 1 is a multiplicative identity? e) How can we conclude from the multiplication table that every non-zero element has an multiplicative inverse relative to 1? 6) Making use of the tables for the field Fs in exercise 5, find the solution to the linear equation 3x +2 = 4, where the coefficients of this equation are considered to be elements of Fg. GONES 7) Find all vectors v in F such that 2v + () 2.
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