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