We have to proof that A+B=B+A we know from defn of matrix addition that (ij )th element of B+A is bij+aij
Since aij &bij are real no's
aij +bij =bij+aij (1
Yes. Matrix addition is commutative.
Let A be a matrix which is both symmetric and skew symmetric. so AT=A and AT= -A so A =- A that implies 2A =zero matrix that implies A is a zero matrix
Let A by an nxn non-singular matrix, then A-1 is the inverse of A. Now (A-1 )-1 =A So the answer is yes.
The assertion is true. Let A be an idempotent matrix. Then we have A.A=A. Since A is invertible, multiplying A-1 to both sides of the equality, we get A = I. Q. E. D
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It is not possible to show that since it is not necessarily true.There is absolutely nothing in the information that is given in the question which implies that AB is not invertible.
A singular matrix is a matrix that is not invertible. If a matrix is not invertible, then:• The determinant of the matrix is 0.• Any matrix multiplied by that matrix doesn't give the identity matrix.There are a lot of examples in which a singular matrix is an idempotent matrix. For instance:M =[1 1][0 0]Take the product of two M's to get the same M, the given!M x M = MSo yes, SOME singular matrices are idempotent matrices! How? Let's take a 2 by 2 identity matrix for instance.I =[1 0][0 1]I x I = I obviously.Then, that nonsingular matrix is also idempotent!Hope this helps!
To do matrix multiplication in calculator Casio fx-991MS follow the steps below:- 1] Enter in the matrix mod:- press MODE 3 times then press 2. 2] To enter the matrix:- press SHIFT and then 4. press 1 to select Dim. to enter the matrix. Suppose u hv to multiply the matri A with matrix B then seletect A by pressing 1 chose dimension for matrix A let m=2 so press 2 then '=' again let n=2 so press 2 then '=' Now, enter the values in matrix MatA11, MatA12, MatA21,MatA22 every time enter the value and then ' =' to enter another values.. remember values get stored in the sequence of row mean 11,21,21,22 now u feel all the values of Matrix A now to enter value of matrix B press SHIFT and again 4. seect Dim by pressing 1. this time chose Mat B and follow the steps same as u use to feel values in matrix A. after entering the values. u stored matrix A and B. 3]Now multiply Matrix A and Matrix B:- press again Shift then 4 and this time select option Mat by pressing 3 to multiply matrix A and matrix B press 1(select Mat A) then press Multiply operator(*/cross). again press Shift then 4 then press 3 and nw selec/press 2(select Mat B) then press '=' 4] you will get the another matrix Ans But the values are in the sequence of row to see next vaues in that matrix press '>' side of REPLAY button.
I'm doing mine Saturday, will let you know after
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They don't let water through.