Equal Matrices
Learn about equal matrices concept. Matrix is the representation of elements in
row and column. If the matrix has m rows and n columns then its order is m x n. If
aij is an element in matrix then a is the element of ith row and jth column. If aij is
element of matrix A and bij is element of matrix B then the matrix A and B are equal
only if a=b for all i and j values. To compare the two matrix the order of the matrix
should be the same.
Definition: Two
matrices are equal if and only if these matrices have the
samedimensions and equal corresponding elements.
If two matrices have their corresponding elements equal, then they are called equal
matrices or.
If then a = p, b = q, c = r and d = s.
Example:
=
Note:
(i) Two equal matrices are exactly the same.
(ii) If rows are changed into columns and columns into rows, we get a transpose
matrix. If the original matrix is A, its transpose is usually denoted by A' or At.
(iii) If two matrices are of the same order (no condition on elements) they are said to
be comparable.
Two matrices are said to be equal if they have the same order and their corresponding
elements are equal.
Example,
then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6.
then a = 2, d = -1, e = 3
Solution: Addition of matrices,
If A and B are 2 matrices of the same order, then A + B is the sum of the 2 matrices
where each element is got by adding corresponding elements of A and B.
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Exercise:
1- Which matrices below are equal?
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Problem 1
Which matrices below are equal?
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Problem 2
Which matrices below are equal?
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Solving for Variables in Matrices
If we know that two matrices are equal, we can find the value
of variables in matrices. Since equal matrices have equal
corresponding entries, we can set an unknown entry in one
matrix equal to its corresponding partner in the other matrix.
To find the value of the variable y in the left hand matrix, we just set it equal to its
corresponding entry in the right hand matrix.
y = 33
Problem 4
Solving for variables in equal matrices will not always be as easy as matching a
variable with a corresponding number. Here's a slightly more challenging
problem: What is the value of y?
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