We are given a matrix A and scalar k, we want to prove that $${(kA)^T} = k{A^T}$$, 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 … [Continue reading]
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 $$({k_1} + {k_2})A = {k_1}A + {k_2}A$$? Two matrices are equal if they have same order and their corresponding elements are equal. Similarly, if we can … [Continue reading]
We have two matrices A, B and scalar k, how to prove that k.(A+B) = kA + KB?
We are given with two matrices A, B of same order and a scalar k. How to prove that $$k(A + B) = kA + kB$$ Two matrices are equal if they have same order and their corresponding elements are equal. Similarly, if we can prove that $$k(A + B)$$ … [Continue reading]
We have two matrices A and B, how to prove that (A+B)^T is equal to A^T + B^T?
How can we prove that $${(A + B)^T} = {A^T} + {B^T}$$ where A and B are two matrices of same order and T represents transpose of matrix. Two matrices are equal if they are of same order and their corresponding elements are equal. In the same way, … [Continue reading]
We are given a matrix A and scalar k then how to prove that adj(KA)=k^n-1(adjA)?
If, we are given a square matrix A then how to prove that $$adj(kA) = {k^{n - 1}}adj(A)$$? where, k is any scalar, adj(A) is adjoint of matrix A and adj(kA) is adjoint of matrix kA. Using formula to find inverse of matrices, we can … [Continue reading]
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