Determinant of any square matrix is equal to determinant of its transpose. Lets take an example of any square matrix and find value of its determinant. Then transpose this matrix and again find value of determinant of transpose of matrix. We will note that determinant of matrix is equal to determinant of its transpose.
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What is symmetric and skew-symmetric matrix?
What is a Symmetric Matrix?
A square Matrix A is said to be symmetric if
for all i and j, where
is an element present at
position (
row and
column in matrix A) and
is an element present at
position (
row and
column in matrix A).
We have matrix A, how to prove that transpose of (A transpose) is equal to matrix A i.e {A^T)^T = A.
We are given matrix A then how can we prove that
. where T represents transpose of Matrix.
Two matrices are said to be equal if they have same order and their corresponding elements are equal. Similarly, to prove
. we will have to prove that both the sides have same order and both the sides have equal corresponding elements.
We are given a matrix A and scalar k, how to prove that (kA)^T = k(A^T)?
We are given a matrix A and scalar k, we want to prove that
, where T represents transpose of matrix.
Two matrices are said to be equal if they have same order and their corresponding elements are equal. Similarly, if we can prove that both the sides of equation
have same order and their corresponding elements are equal then it means equation
is true.
We are given with a matrix A and two scalars k1, k2, how to prove that (k1+k2)A = k1A + k2A?
We are given with a matrix A and two scalars k1 and k2, how can we prove that
?
Two matrices are equal if they have same order and their corresponding elements are equal.
Similarly, if we can prove that
and
have same order and their corresponding elements are equal then it means equation
is true.
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