Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# 2.1 - Matrix Operations •Denoting a general matrix A of m rows and n columns Example: •So matrix addition and scalar multiplication are component‐wise.
•Exercise: Write a sum of two general matrices A, B Properties of Addition & Scalar Mult

• If A, B, C are the same size, r, s any scalars,
then
• A+ B=B+ A • (A+ B) +C=A+ (B+C) • A+0=A if 0 is the matrix of the same size, consisting
of all 0’s •Other facts on p 108, Th 1 How to write a proof of a matrix fact

•Commutative property (A+ B=B+ A)   Matrix Multiplication

• We have already seen when we can multiply AB.
• Review how it works   Matrix Multiplication – General Case

•Use the columns of B
(In text)

•General rule (without columns) – p 111 Computing a specific row/column of a product · Find Properties of Matrix Multiplication

•P 113, Th 2
•Associative •Left Distributive
•Right Distributive
•Scalar multiples • Identity •Note what’s missing! Verify. Transpose AT

• Definition  Properties of AT

•Page 115 (Th 3) 