Friday, March 22, 2013

Find each of the following: (i) A + B (ii) A – B (iii) 3A – C (iv) AB (v) BA

Let A =
[
2
4
]
, B =
[
1
3
]
, C=
[
-2
5
]
3
2
-2
5
3
4

Find each of the following:
(i)         A + B   (ii) A – B         (iii) 3A – C      (iv) AB            (v) BA

(i) Find the sum of matrix
[
2
4
]
+
[
1
3
]

A+ B =
3
2
-2
5



[
2+1
4+3
]

A+ B =
3+(-2)
2+5



A+B =
[
3
7
]

1
7


(ii) A - B
[
2
4
]
-
[
1
3
]

(ii)A -  B =
3
2
-2
5


Subtract 
corresponding
elements

[
2-1
4-3
]

A -  B =
3-(-2)
2-5



A - B =
[
1
1
]

5
-3



  








(iii) 3A -C
[
2
4
]
-
[
-2
5
]
3A -  C =
3
2
3
4
multiply matrix A with 3 and subtract matrix C
[
3x2-(-2)
3x4-(5)
]
3A -  C =
3x3-(3)
3x2-(4)
3A - C =
[
8
7
]
6
2


(iv) AB
[
2
4
]
[
1
3
]
A=
3
2
B=
-2
5
rows =
3
column =
2
rows =
2
column =
2

Condition of multiplication

To multiply two matrices, number of columns of first matrix should be equal to number of rows of second matrix and in our matrix number of columns first matrix is 2 and number of rows of second matrix is  2  and both values are equal so multiplication of both matrix is possible




Order of new matrix
Order of new matrix will equal to rows of first matrix by columns of second matrix and number of rows are equal to 3 and number of columns are 2 hence order of new matrix will 2x2


A=
[
2
4
]
B=
[
1
3
]
3
2
-2
5
AB=
[
2 x (1) + 4 x ( -2)
2 x (3) + 4 x ( 5)
]

3 x (1) + 2 x ( -2)
3 x (3) + 2 x ( 5)


AB=
[
2 + (-8)
6 + (20)
]

3 + (-4)
9 + (10)


AB=
[
-6
26
]
-1
19


(v) BA
[
1
3
]
[
2
4
]
A=
-2
5
B=
3
2
rows =
3
column =
2
rows =
2
column =
2
Condition of multiplication
To multiply two matrices, number of columns of first matrix should be equal to number of rows of second matrix and in our matrix number of columns first matrix is 2 and number of rows of second matrix is  2  and both values are equal so multiplication of both matrix is possible
Order of new matrix
Order of new matrix will equal to rows of first matrix by columns of second matrix and number of rows are equal to 3 and number of columns are 2 hence order of new matrix will 2x2
A=
[
1
3
]
B=
[
2
4
]
-2
5
3
2
BA=
[
1 x (2) + 3 x ( 3)
1 x (4) + 3 x ( 2)
]
-2 x (2) + 5 x ( 3)
-2 x (4) + 5 x ( 2)
BA=
[
2 + (9)
4 + (6)
]
-4 + (15)
-8 + (10)
]
BA=
[
11
10
11
2

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