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Chapter 7 part 1 - Math for business | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

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Chapter 7 part 1 - Math for business | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

55 28 lượt tải Tải xuống

Math for business Contact: ngominhtuyetngoc216@gmail.com

Chapter 7: Matrices

I. BASIC MATRIX OPERATIONS

1. Definition:

- Matrix A has m rows and n columns

→ matrix order m x n

- Ex: Matrix A (3 x 2): a a a

11 12 13

a a

22 23

- m = 1, n = 0 row vector →

n = 1, m = 0 column vector →

2. Transposition:

- Matrix A (m x n) The transposition of A →

is A

is found by replacing rows by columns

Ex: A = A = →

3. Addition and subtraction

- Condition: same order

- Matrix A: a a a

11 12 13

a a

22 23

Matrix B: b b

11 12

- C = A + B C: c c c 

11 12 13

c c

22 23

= a + b ; c = a + b

11 11 12 12 12.

; …

- A − A = 0

A + 0 = A

4. Scalar multiplication

- Multiply a matrix A by a scalar k:

kA = ka ka ka

11 12 13

ka ka

22 23

k (A + B) = kA + kB

k(lA) = (kl)A

5. Matrix multiplication.

- A (m x n ) and B (m x n

A A B B

)

 C = A x B - condition: n = m

A B

C = B x A - condition: n = m

B A

➔ AB ≠ BA

- Method:

------------------------------------------------------------------------

II. BASIC MATRIX OPERATIONS

----------------------------------------------------------------------

---------------------------------------------------------------------

7 3 4

1 5 6

7 1

3 5

4 6

Math for business Contact: ngominhtuyetngoc216@gmail.com

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Chapter 7: Matrices I.
BASIC MATRIX OPERATIONS 1. Definition: - A − A = 0 -
Matrix A has m rows and n columns A + 0 = A → matrix order m x n
4. Scalar multiplication - Ex: Matrix A (3 x 2): a11 a12 a13 -
Multiply a matrix A by a scalar k: a21 a22 a23 kA = ka11 ka12 ka13 - m = 1, n = 0 → row vector ka21 ka22 ka23
n = 1, m = 0 → column vector -
k (A + B) = kA + kB
2. Transposition:
k(lA) = (kl)A -
Matrix A (m x n) → The transposition of A
5. Matrix multiplication. is AT - A (mA x nA) and B (mB x nB) -
AT is found by replacing rows by columns
 C = A x B - condition: nA = mB - Ex: A = 7 3 4 → AT =
C = B x A - condition: nB = mA 7 1 ➔ AB ≠ BA 1 5 6 - Method: 3 5
------------------------------------------------------------------------ 4 6
------------------------------------------------------------------------
3. Addition and subtraction
------------------------------------------------------------------------ - Condition: same order
------------------------------------------------------------------------
------------------------------------------------------------------------ - Matrix A: a11 a12 a13
------------------------------------------------------------------------ a21 a22 a23
------------------------------------------------------------------------ Matrix B: b11 b12
------------------------------------------------------------------------ b13
------------------------------------------------------------------------ b21 b22
------------------------------------------------------------------------ b
------------------------------------------------------------------------ 23 - C = A + B
------------------------------------------------------------------------  C: c11 c12
c13 ------------------------------------------------------------------------ c21 c22 c23
c11 = a11 + b11; c12 = a12 + b12.; … II.
BASIC MATRIX OPERATIONS
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