Construct a Matrix With Given Order :
In this section, you will learn how to construct a matrix with the order given.
Question 1 :
Construct an m × n matrix A = [a_{ij}], where a_{ij} is given by
(i) a_{ij} = (i - 2j)^{2}/2 with m = 2 and n = 3
Solution :
In general, a 2 x 3 is given by A =
General term :
a_{ij} = (i - 2j)^{2}/2
i = 1 and j = 1 a_{11} = (1 - 2)^{2}/2 = (-1)^{2}/2 = 1/2 |
i = 1 and j = 2 a_{12} = (1 - 4)^{2}/2 = (-3)^{2}/2 = 9/2 |
i = 1 and j = 3 a_{13} = (1 - 6)^{2}/2 = (-5)^{2}/2 = 25/2 |
i = 2 and j = 1 a_{21} = (2 - 2)^{2}/2 = 0/2 = 0 |
i = 2 and j = 2 a_{21} = (2 - 4)^{2}/2 = 4/2 = 2 |
i = 2 and j = 3 a_{21} = (2 - 6)^{2}/2 = 16/2 = 8 |
Hence the required matrix with order 2 x 3 is
(ii) a_{ij} = |3i - 4j|/4 with m = 3 and n = 4
Solution :
In general, a .3 x 4 is given by A =
General term :
a_{ij} = |3i - 4j|/4
i = 1 and j = 1 a_{ij} = |3i - 4j|/4 a_{11} = |3 - 4|/4 = 1/4 |
i = 1 and j = 2 a_{ij} = |3i - 4j|/4 a_{12} = |3 - 8|/4 = 5/4 |
i = 1 and j = 3 a_{ij} = |3i - 4j|/4 a_{12} = |3 - 12|/4 = 9/4 |
i = 1 and j = 4 a_{ij} = |3i - 4j|/4 a_{12} = |3 - 16|/4 = 13/4 |
i = 2 and j = 1 a_{ij} = |3i - 4j|/4 a_{21} = |6 - 4|/4 = 2/4 = 1/2 |
i = 2 and j = 2 a_{ij} = |3i - 4j|/4 a_{21} = |6 - 8|/4 = 2/4 = 1/2 |
i = 2 and j = 3 a_{ij} = |3i - 4j|/4 a_{21} = |6 - 12|/4 = 6/4 = 3/2 |
i = 2 and j = 4 a_{ij} = |3i - 4j|/4 a_{21} = |6 - 16|/4 = 10/4 = 5/2 |
i = 3 and j = 1 a_{ij} = |3i - 4j|/4 a_{31} = |9 - 4|/4 = 5/4 |
i = 3 and j = 2 a_{ij} = |3i - 4j|/4 a_{32} = |9 - 8|/4 = 1/4 |
i = 3 and j = 3 a_{ij} = |3i - 4j|/4 a_{33} = |9 - 12|/4 = 3/4 |
i = 3 and j = 4 a_{ij} = |3i - 4j|/4 a_{34} = |9 - 16|/4 = 7/4 |
Hence the required matrix with order 3 x 4 is
After having gone through the stuff given above, we hope that the students would have understood how to construct a matrix with the order given.
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