If matrix A=[ 3 −3
−3 3], and 2 = , then find the value of k.
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Step-by-step explanation:
3.1.1 A matrix is an ordered rectangular array of numbers (or functions). For example,
A =
4 3
4 3
3 4
x
x
x
The numbers (or functions) are called the elements or the entries of the matrix.
The horizontal lines of elements are said to constitute rows of the matrix and the
vertical lines of elements are said to constitute columns of the matrix.
3.1.2 Order of a Matrix
A matrix having m rows and n columns is called a matrix of order m × n or simply
m × n matrix (read as an m by n matrix).
In the above example, we have A as a matrix of order 3 × 3 i.e.,
3 × 3 matrix.
In general, an m × n matrix has the following rectangular array :
A = [aij]m × n
= 11 12 13 1
21 22 23 2
1 2 3 ×
n
n m m m mn m n a a a a
a a a a
a a a a
1≤ i ≤ m, 1≤ j ≤ n i, j ∈ N.
The element, aij is an element lying in the i
th row and j
th column and is known as the
(i, j)
th element of A. The number of elements in an m × n matrix will be equal to mn. 3.1.3 Types of Matrices
(i) A matrix is said to be a row matrix if it has only one row.