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A rectangular array of numbers arranged in horizontal and vertical enclosed between round (or square) brackets is called the matrix. Horizontal lines are called rows and vertical lines are called column of the matrix.
The order or the size of the matrix is given by the number of rows followed by the number of columns. If a matrix contains m rows and n columns, then it is of order m×n, read as m by n.
\(\begin{pmatrix} 2&6\\4&3\end{pmatrix}\) is a 2x2 matrix and\(\begin{pmatrix} 2&3&4\\5&2&9\end{pmatrix}\) is a 3x3 matrix.
A matrix of order m×n has mn elements.
The matrices are usually denoted by a capital letter such as A, B, C,....etc. The elements are denoted by the corresponding small letters along with two suffixes. The first suffix indicates the number of rows and the latter one indicates the number of columns in which the element appears.
a_{ij} is the element of a matrix A in the i^{th} row and j^{th} column.
a_{23} is the element of a matrix A in the 2^{nd} row and 3^{rd} column.
Thus, a matrix of order m×n may be written as
A =(a_{ij})m×n.
If A is a 3x3 matrix, then it may be written as
A=\(\begin{bmatrix} a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{bmatrix}\)
Two matrices A&B are said to be equal matrices if A and B are of some order i.e. number of rows in A = number of rows in B and number of columns in A = number of columns in B, and their corresponding elements are equal i.e. the entries of A and B in some position are equal. Otherwise, the matrices are said to be unequal. If A and B equal matrices, then we write A=B. Otherwise, we write A ≠B.
Soln:
here given matrix,
B=\(\begin{bmatrix} 20 & 35 & 55 & 70 \\ 25 & 45 & 60 & 75 \\ 30 & 50 & 65 & 80 \\ \end{bmatrix}\)
(a) In matrix B, there are 12 elements in 3 rows and 4 columns.
(b) There are 3 rows and 4 columns. So, its size is 3×4.
It is written in the order nation as B_{3×4} or, \(\begin{bmatrix} 20 & 35 & 55 & 70 \\ 25 & 45 & 60 & 75 \\ 30 & 50 & 65 & 80 \\ \end{bmatrix}\)3×4
soln:
Here given matrices,
\(\begin{pmatrix} 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ \end{pmatrix}\) and \(\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0\\ 0 & 0 & 0 \\ \end{pmatrix}\). Both of these two matrices are null matrix but they are not equal size.
If (egin{pmatrix} a&b\ c&d\ end{pmatrix})- (egin{pmatrix} 1&2\ 3&4\ end{pmatrix})= (egin{pmatrix} 5&6\ 7&8\ end{pmatrix}) then find the values of a,b,c and d.
If (egin{pmatrix} 5&3\ a&0\ end{pmatrix})= (egin{pmatrix} b&4\ 2&6\ end{pmatrix})+ (egin{pmatrix} 2&-1\ 2a&-6\ end{pmatrix}), find the values of a and b.
-1,5
-2,3
2,3
4,5
If A (egin{pmatrix} 5&1&2\ 6&3&4\ end{pmatrix}),find the value of a_{12}+a_{13}-a_{22}.
one
two
zero
three
If P (egin{pmatrix} 3&4&5\ 6&7&8\ end{pmatrix}) then find the value of a_{12}×a_{21}÷a_{23}.
In each of the following conditions, find the values of x and y:
2[3 x]+[y -2] =[4 1]+[2 1]
4,6
2,0
5,5
1,3
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