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

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23 12 lượt tải Tải xuống
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Môn: Math for business

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

Thông tin:

3 trang 4 tháng trước

Tác giả:

Profile Mai Nguyệt
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
21
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
T
-
A
T
is found by replacing rows by columns
-
Ex: A = A = →
T
3. Addition and subtraction
- Condition: same order
- Matrix A: a a a
11 12 13
a
21
a a
22 23
Matrix B: b b
11 12
b
13
b
21
b
22
b
23
- C = A + B C: c c c
11 12 13
c
21
c c
22 23
c
11
= 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
21
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:
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II. BASIC MATRIX OPERATIONS
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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
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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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--------------------------------------------------------------------- Math for business
Contact: ngominhtuyetngoc216@gmail.com