What is the top-left entry in the matrix a4 where a 3 b c

Question

Question 1

D is the matrix given by

D =	h	0
	0	k

where h = 36 and k = -4. What is the lower-light entry in the matrix Dⁿ, where n = 6?

Question 2

The matrix A is given by

A=	a	b
	c	d

where a = 6, b = -21, c = -6 and d = -12. The matrix A has two eigenvalues h and k, where h > k. To 2 decimal places, what is the value of h?

Question 3

A=	a	b
	c	d

where a = -6, b = 8, C = 6 and d = -6.

What is the top-left entry in the matrix A⁴?

Question 4

A conic has equation

ay² + bx = 0

where a = 13 and 13 = -296. If the focus point is at (F, 0) then what is the value of F to 2 decimal places?

Question 5

An ellipse has equation ax² + by² = c

where a = 19, b= 39 and c = 269. One of the vertices; (0, d), lies on the positive y-axis. To 2 decimal places, what is the value of d?

Question 6

The matrix A is given by

A=	a	b
	c	d

where a = 3, b = c = -5 and d = -18. The matrix A has two eigenvalues h and Is. where h > k. To 2 decimal places, what is the gradient of the eigenline that corresponds to eigenvalue h?