Matrix Operations
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A matrix is a rectangular arrangement of numbers organized in rows and columns. The order of a matrix refers to the number of rows and columns it contains. Entries are the individual numbers within the matrix. Basic matrix operations include addition, subtraction, scalar multiplication, and multiplication. To add or subtract matrices, they must be the same order, while scalar multiplication multiplies each entry of the matrix by the scalar.
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−−
−
67237
89511
36402
−
−
3410
200
318 [ ]0759 −
−
20
11
−
6
0
7
9
3 x 3
3 x 5
2 x 2 4 x 1
1 x 4
(or square
matrix)
(Also called a
row matrix)
(or square
matrix)
(Also called a
column matrix)](https://image.slidesharecdn.com/matrixpart2-140315181645-phpapp01/85/Matrix-Operations-3-320.jpg)
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3108
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=
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[ 7 7 4 5
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−
−
724
113
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051
708
342
[ []=
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8-3 0-(-1) -7-1
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5 3 -7
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86
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2
−++
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−=
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5241
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−
−
+
−
−
86
54
30
21
2
−++
+−−
−=
)8(360
5241
2
=
[ [
[ ]
]]
-2
6
-3 3
-2(-3)
-5
==
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-2(3) 6 -6
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Matrix Operations
- 2. MATRIX:MATRIX: A rectangularA rectangular arrangement ofarrangement of numbers in rows andnumbers in rows and columns.columns. TheThe ORDERORDER of a matrixof a matrix is the number of theis the number of the rows and columns.rows and columns. TheThe ENTRIESENTRIES are theare the numbers in the matrix.numbers in the matrix. − − 502 126 rows columns This order of this matrixThis order of this matrix is a 2 x 3.is a 2 x 3.
- 3. −− − 67237 89511 36402 − − 3410 200 318 [ ]0759 − − 20 11 − 6 0 7 9 3 x 3 3 x 5 2 x 2 4 x 1 1 x 4 (or square matrix) (Also called a row matrix) (or square matrix) (Also called a column matrix)
- 4. To add two matrices, they must have the sameTo add two matrices, they must have the same order. To add, you simply add correspondingorder. To add, you simply add corresponding entries.entries. − − + − − 34 03 12 70 43 35 −++ ++− +−−+ = )3(740 0433 13)2(5 − = 44 40 23
- 5. + − − 9245 3108 − − 2335 2571 [ ])1(8 −+ 70 + 51+− 23+ 55+− 34+ 32+ )2(9 −+ = = [ 7 7 4 5 0 7 5 7 ]
- 6. To subtract two matrices, they must have the sameTo subtract two matrices, they must have the same order. You simply subtract corresponding entries.order. You simply subtract corresponding entries. − −− − 232 451 704 831 605 429 −−−− −−−− −−−− = 2833)2(1 )4(65015 740249 − −− = 603 1054 325
- 7. − −− − − 724 113 810 051 708 342 [ []= 5-2 -4-1 3-8 8-3 0-(-1) -7-1 1-(-4) 2-0 0-7 = 2 -5 -5 5 1 -8 5 3 -7 ]
- 8. In matrix algebra, a real number is often called aIn matrix algebra, a real number is often called a SCALARSCALAR.. To multiply a matrix by a scalar, you multiply each entry inTo multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar.the matrix by that scalar. − − 14 02 4 − − = 416 08 − − = )1(4)4(4 )0(4)2(4
- 9. − − + − − 86 54 30 21 2 −++ +−− −= )8(360 5241 2 = [ [ [ ] ]] -2 6 -3 3 -2(-3) -5 == -2(6) -2(-5) -2(3) 6 -6 -12 10
- 10. − − + − − 86 54 30 21 2 −++ +−− −= )8(360 5241 2 = [ [ [ ] ]] -2 6 -3 3 -2(-3) -5 == -2(6) -2(-5) -2(3) 6 -6 -12 10