Introduction to matrices algebra 1.
An rectangular arrangement of numbers in rows and columns within the paranthesis is called a matrix. If there are m rows and n columns in a matrix then m `xx` n is called order of the matrix. In this topic let us know three operations on the given matrices.
Two matrices A and B can be added or subtracted if their orders are same. If not matrix addition or subtraction is not defined.
Two matrices can be multiplied if the number of column in the first matrix is equal to the number of rows in the second matrix. Otherwise the matrix multiplication is not defined.
Now let us see few problems in this topic matrices algebra 1
Examples of Matrices Algebra 1
Ex 1: Find the sum of the given matrices A and B.
A = `[[1,2],[3,4]]` and B = `[[5,7],[6,8]]`
Soln: Since A and B are having same orders 2 `xx` 2,
A + B = `[[1,2],[3,4]]` + `[[5,7],[6,8]]`
= `[[1+5,2+7],[3+6,4+8]]` [Add the corresponding values]
Therefore A + B = `[[6,9],[9,12]]`
Ex 2: Find the value of the given equation 2A – B.
Here A = `[[4,6],[7,5]]` and B = `[[3,2],[1,4]]`
Soln: 2A – B = 2 `[[4,6],[7,5]]` - `[[3,2],[1,4]]`
= `[[2xx4, 2xx6],[2xx7,2xx5]]` - `[[3,2],[1,4]]`
= `[[8,12],[14,10]]` `[[3,2],[1,4]]`
= `[[8**3, 12**2],[14**1,10**4]]` [Subtract the corresponding values]
= `[[5,10],[13,6]]`
Therefore 2A – B =` [[5,10],[13,6]]`
More Example Problems on Matrices Algebra 1
Ex 3: Multiply the following matrices if possible:
(i) A = `[[2,3,4],[5,6,7]]` and B = `[[2,7],[5,6]]`
(ii) A = `[[3,4],[2,8]] ` and B = `[[7,2],[1,8]]`
Soln: (i) The order of matrix
A = `[[2,3,4],[5,6,7]]` is 2 `xx` 3and B = `[[2,7],[5,6]]`
For B, it is 2 `xx` 2.
Here the number of column in A is not equal to the number of rows in B (3≠ 2). Therefore AB is not possible.
(ii) Here in A and B, the number columns in A is equal number of rows in B (2=2). Therefore AB is possible
Therefore AB = `[[3,4],[2,8]] ` `[[7,2],[1,8]]`
= `[[3 xx 7 + 4 xx 1,3 xx 2 + 4 xx 8],[2 xx 7 + 8 xx 1,2 xx 2 + 8 xx 8]]`
= `[[21 + 4,6 + 32],[14 + 8,4 + 64]]`
= `[[25,38],[22,68]]`
An rectangular arrangement of numbers in rows and columns within the paranthesis is called a matrix. If there are m rows and n columns in a matrix then m `xx` n is called order of the matrix. In this topic let us know three operations on the given matrices.
Two matrices A and B can be added or subtracted if their orders are same. If not matrix addition or subtraction is not defined.
Two matrices can be multiplied if the number of column in the first matrix is equal to the number of rows in the second matrix. Otherwise the matrix multiplication is not defined.
Now let us see few problems in this topic matrices algebra 1
Examples of Matrices Algebra 1
Ex 1: Find the sum of the given matrices A and B.
A = `[[1,2],[3,4]]` and B = `[[5,7],[6,8]]`
Soln: Since A and B are having same orders 2 `xx` 2,
A + B = `[[1,2],[3,4]]` + `[[5,7],[6,8]]`
= `[[1+5,2+7],[3+6,4+8]]` [Add the corresponding values]
Therefore A + B = `[[6,9],[9,12]]`
Ex 2: Find the value of the given equation 2A – B.
Here A = `[[4,6],[7,5]]` and B = `[[3,2],[1,4]]`
Soln: 2A – B = 2 `[[4,6],[7,5]]` - `[[3,2],[1,4]]`
= `[[2xx4, 2xx6],[2xx7,2xx5]]` - `[[3,2],[1,4]]`
= `[[8,12],[14,10]]` `[[3,2],[1,4]]`
= `[[8**3, 12**2],[14**1,10**4]]` [Subtract the corresponding values]
= `[[5,10],[13,6]]`
Therefore 2A – B =` [[5,10],[13,6]]`
More Example Problems on Matrices Algebra 1
Ex 3: Multiply the following matrices if possible:
(i) A = `[[2,3,4],[5,6,7]]` and B = `[[2,7],[5,6]]`
(ii) A = `[[3,4],[2,8]] ` and B = `[[7,2],[1,8]]`
Soln: (i) The order of matrix
A = `[[2,3,4],[5,6,7]]` is 2 `xx` 3and B = `[[2,7],[5,6]]`
For B, it is 2 `xx` 2.
Here the number of column in A is not equal to the number of rows in B (3≠ 2). Therefore AB is not possible.
(ii) Here in A and B, the number columns in A is equal number of rows in B (2=2). Therefore AB is possible
Therefore AB = `[[3,4],[2,8]] ` `[[7,2],[1,8]]`
= `[[3 xx 7 + 4 xx 1,3 xx 2 + 4 xx 8],[2 xx 7 + 8 xx 1,2 xx 2 + 8 xx 8]]`
= `[[21 + 4,6 + 32],[14 + 8,4 + 64]]`
= `[[25,38],[22,68]]`
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