page 57

Multiply											ANS.
1 2 3					10					=						1 2 3					10			=				68
4 5 6					11											4 5 6					11							167
7 8 9					12											7 8 9					12							266
Determinant
							=						1 2 3								= 36
	1 2 3
	4 2 6												4 2 6
	7 8 9												7 8 9
Inverse																			–1
					–1									1 2 3											–0.833					0.167	0.167
	1 2 3																				=
					=									4 2 6											0.167					–0.333	0.167
	4 2 6
														7 8 9													0.5			0.167	–0.167
	7 8 9

2.	Perform the vector operations below,
											ANS.
	A =	1			B =	6			Cross Product	A ×B =
											A ×B = (–4,17 ,–10 )
		2				2
		3				1			Dot Product	A •B =	A •B = 13
4.	Solve the following equations using any technique,

5x – 2y + 4z = –1 6x + 7y + 5z = –2 2x – 3y + 6z = –3

ANS.

x= 0.273 y= -0.072 z= -0.627

2.6 CALCULUS

• NOTE: Calculus is very useful when looking at real systems. Many students are turned off by the topic because they "don’t get it". But, the secret to calculus is to remember that there is no single "truth" - it is more a loose collection of tricks and techniques. Each one has to be learned separately, and when needed you must remember it, or know where to look.