3a A transformation is defined by the 2 x 2 matrix -a b - a A la +b a where a and b are scalars. If n is an odd integer, prove that A" 3b 4 - 2x A В f (x) %3D (x+1)(x+3)(2.x + 1) (x+ 1) (x+3) (2x+1) find the values of A,B,C 3c The point A has coordinates (-3, 2) and the point B has coordinates (7, k). The line AB has equation Зх + 5у 3D 1 i Show thatk = -4 ii Find the coordinates of the mid-point of AB iii Find the gradient of AB
3a A transformation is defined by the 2 x 2 matrix -a b - a A la +b a where a and b are scalars. If n is an odd integer, prove that A" 3b 4 - 2x A В f (x) %3D (x+1)(x+3)(2.x + 1) (x+ 1) (x+3) (2x+1) find the values of A,B,C 3c The point A has coordinates (-3, 2) and the point B has coordinates (7, k). The line AB has equation Зх + 5у 3D 1 i Show thatk = -4 ii Find the coordinates of the mid-point of AB iii Find the gradient of AB
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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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
Solve 3a, 3b and 3c respectively.
Transcribed Image Text:3a A transformation is defined by the 2 × 2 matrix
-a
b — а
A
a + b
a
where a and b are scalars. If n is an odd integer, prove that
A" =
bn-1 A
3b
4 – 2.x
A
В
C
f (x)
(x+1)(x + 3)(2x + 1)
+
(x+ 3)
(x +1)
(2х + 1)
find the values of A,B,C
3c The point A has coordinates (–3, 2) and the point B has coordinates (7, k). The line AB has equation
Зх + 5y — 1
i Show that k = -4
ii Find the coordinates of the mid-point of AB
iii Find the gradient of AB
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