Chapter 7

Question 1

Adding and subtracting matrices

Answer 1

Add or subtract each corresponding number. NUMBER OF ROWS AND COLUMNS MUST BE THE SAME!

Question 2

Multiplying matrices

Answer 2

number of columns must = number of rows of second matrix:

Multiply first column by both rows to get top two numbers then second column by both rows to get bottom two numbers. this is fro 2x2 times a 3x2

Question 3

Identity matrix

Answer 3

equal to 1 on all diagonal elements and 0 Everywhere else

Question 4

Taking the determinant

Answer 4

cross multiply: ad-bc for 2x2
for 3x3 take each top number, cover all other numbers in row and column as that number. take determinant of the remaining matrix them multiply that by the original number. do this for all numbers and subtract them all.

Question 5

Requirements of a field

Answer 5

FOR BOTH ADDITION AND MULTIPLICATION:

• closure
• associative
• commutative
• identity
• inverse
• distribution