In Problems 53 - 56 , (A) Graph f and g in the same coordinate system . (B) Solve f x = g x algebraically to two decimal places. (C) Solve f x > g x using parts A and B (D) Solve f x < g x using parts A and B f x = − 0.4 x x − 10 g x = 0.3 x + 5 0 ≤ x ≤ 10
In Problems 53 - 56 , (A) Graph f and g in the same coordinate system . (B) Solve f x = g x algebraically to two decimal places. (C) Solve f x > g x using parts A and B (D) Solve f x < g x using parts A and B f x = − 0.4 x x − 10 g x = 0.3 x + 5 0 ≤ x ≤ 10
Solution Summary: The author explains how to graph the functions f(x)=-0.4x-left (x-10 ) and
(B) Solve
f
x
=
g
x
algebraically to two decimal places.
(C) Solve
f
x
>
g
x
using parts
A
and
B
(D) Solve
f
x
<
g
x
using parts
A
and
B
f
x
=
−
0.4
x
x
−
10
g
x
=
0.3
x
+
5
0
≤
x
≤
10
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Let A be a vector space with basis 1, a, b. Which (if any) of the following rules
turn A into an algebra? (You may assume that 1 is a unit.)
(i) a² = a, b² = ab = ba = 0.
(ii) a²=b, b² = ab = ba = 0.
(iii) a²=b, b² = b, ab = ba = 0.
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= 1. Show
(a) Let G = Z/nZ be a cyclic group, so G = {1, 9, 92,...,g" } with g":
that the group algebra KG has a presentation KG = K(X)/(X” — 1).
(b) Let A = K[X] be the algebra of polynomials in X. Let V be the A-module
with vector space K2 and where the action of X is given by the matrix
Compute End(V) in the cases
(i) x = p,
(ii) xμl.
(67) ·
(c) If M and N are submodules of a module L, prove that there is an isomorphism
M/MON (M+N)/N.
(The Second Isomorphism Theorem for modules.)
You may assume that MON is a submodule of M, M + N is a submodule of L
and the First Isomorphism Theorem for modules.
Chapter 2 Solutions
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