Find the kernel and range of each of the following linear operators on P 3 : (a) L ( p ( x ) ) = x p ' ( x ) (b) L ( p ( x ) ) = p ( x ) − p ' ( x ) (c) L ( p ( x ) ) = p ( 0 ) x + p ( 1 )
Find the kernel and range of each of the following linear operators on P 3 : (a) L ( p ( x ) ) = x p ' ( x ) (b) L ( p ( x ) ) = p ( x ) − p ' ( x ) (c) L ( p ( x ) ) = p ( 0 ) x + p ( 1 )
Find the kernel and range of each of the following linear operators on
P
3
: (a)
L
(
p
(
x
)
)
=
x
p
'
(
x
)
(b)
L
(
p
(
x
)
)
=
p
(
x
)
−
p
'
(
x
)
(c)
L
(
p
(
x
)
)
=
p
(
0
)
x
+
p
(
1
)
Find the linearization of the function at x = 1. *
f (x)
2x – 3x + 7
O y = 6 + 1(x - 3)
O y = 6 + 3(x - 1)
O y = 1+ 3(x - 6)
O y = 3 + 6(x - 1)
Suppose that the functions s and t are defined for all real numbers x as follows.
s (x) =
I (x) =2x²
x+1
Write the expressions for (t+s) (x) and (t-s) (x) and evaluate (t's) (2).
(1+ s)(x) = 0
%3D
(1 - s)(x) = 0
(1-s)(2) = ]
For #'s 11-14 , h(x) = (f og)(x)
Let h(x) = (2x–5) and f(x)=x', find g(x)
Let h(x) = Vx-5 and f(x)= Vx, find g(x)
Let h(x)= (5x + 1) -(5x +1) and S(x) = x² – x, find g(x)
11.
12.
13.
14.
Let h(x) = V(-3x – 2) and f(x) = vx, find g(x)
Chapter 4 Solutions
Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
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