Definition of a Matrix - Matrices and Determinants, Business Mathematics & Statistics Video Lecture | Business Mathematics and Statistics - B Com

0:0:3: 1, 3, minus 5 and 8.
0:0:6: This is just a row of four numbers
0:0:8: and this can be represented in different ways.
0:0:12: We can write it as an array of numbers horizontally like this
0:0:16: or we can write it as an array of numbers vertically like this.
0:0:20: The first part as you can see has one row and four columns
0:0:24: and the second part has four rows and one column.
0:0:28: There's another way in which we can write the four numbers.
0:0:31: The first two numbers in the first row
0:0:33: and the last two numbers in the second row.
0:0:36: All these three things you see here are called matrices.
0:0:40: Each of these is a Matrix.
0:0:43: Just an arrangement of rows and columns.
0:0:46: But how do we properly define it?
0:0:49: We can say that a matrix is a rectangular arrangement.
0:0:52: But a rectangular arrangement of what?
0:0:55: It can be anything.
0:0:57: Numbers, letters or the characters. Anything.
0:1:1: A Matrix is made up of rows and column.
0:1:4: The first Matrix has one row and four columns.
0:1:7: The second one has four rows and one column.
0:1:11: And what about the third one?
0:1:13: It has two rows and 2 columns.
0:1:15: So a matrix is just a rectangular arrangement of rows and columns
0:1:20: But there is one important condition we need to keep in mind.
0:1:24: Each row needs to have equal number of elements.
0:1:27: For instance in the second Matrix,
0:1:29: each row has one element.
0:1:32: And in the third matrix each row has two elements.
0:1:35: And each column also needs to have equal number of elements.
0:1:40: In the first Matrix each column has one element,
0:1:43: the second Matrix has just one column so it doesn't matter
0:1:47: and in the third one each column has two elements.
0:1:51: So a matrix is a
0:1:52: rectangular arrangement of rows and columns
0:1:55: in which each row has equal number of elements
0:1:58: and each column as well has equal number of elements.
0:2:2: So is this a Matrix?
0:2:3: Elements 'a' and 'b' in the first row
0:2:6: and elements 'c' and 'd' in the second.
0:2:9: It is a rectangular arrangement.
0:2:11: Each row has two elements
0:2:12: and each column has two elements.
0:2:14: It is a Matrix!
0:2:16: And these three are also Matrices.
0:2:20: Okay, what about this one with three elements?
0:2:23: Is it a matrix?
0:2:24: The first row has two elements
0:2:26: but the second one has just has one element.
0:2:29: So it is not a matrix.
0:2:31: What about this one with five elements?
0:2:33: The number of elements in each of the columns
0:2:36: is not the same.
0:2:37: It's 2, 1 and 2 and this as well is not a matrix.
0:2:42: So this is the definition.
0:2:44: A rectangular arrangement of rows and columns in
0:2:47: which each row should have equal number of elements
0:2:50: and each column as well.
0:2:52: should have equal number of elements.