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Prove that a matrix which is both symmetric as well as skew symmetric is a null matrix?
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
Is Inverse of the inverse matrix the original 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.
Is an invertible idempotent matrix the identity matrix?
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
Prove that a matrix a is singular if and only if it has a zero eigenvalue?
Recall that if a matrix is singular, it's determinant is zero. Let our nxn matrix be called A and let k stand for the eigenvalue. To find eigenvalues we solve the equation det(A-kI)=0for k, where I is the nxn identity matrix. (<==) Assume that k=0 is an eigenvalue. Notice that if we plug zero into this equation for k, we just get det(A)=0. This means the matrix is singluar. (==>) Assume that det(A)=0. Then as stated above we need to find solutions of the equation det(A-kI)=0. Notice that k=0 is a solution since det(A-(0)I) = det(A) which we already know is zero. Thus zero is an eigenvalue.
How do you multiply 3x3 matrices by 1x3 or 3x1?
First of all, if we have any two matrices of sizes mxn and pxq where m, n, p and q are natural numbers, then we must have n=p to be able to multiply the matrices. The result is an mxq matrix. For example, a 3x1 matrix has m=3 and n=1. We can multiply it with any matrix of size 1xq. For example a 2x3 matrix can be multiplied with a 3x1 matrix which has 3 rows and 1 column and the result is a 2x1 matrix. (2x3) multiplies by (3x1) gives a (2x1) matrix. The easy way to remember this is write the dimension of Matrix A and then Matrix B. The two inner numbers must be the same and the two outer numbers are the dimensions of the matrix you have after multiplication. For example Let Matrix A have dimensions (axb) multiply it by matrix B which has dimensions (bxc) = the result is matrix of dimensions ac. Using the trick we would remind ourselves by writing (a,b)x(b,c)=(a,c). This is technically wrong because the numbers are dimensions, but it is just a method to help students remember how to do it. So, a 3x3 matrix can be multiplied by a 3x 1 but not by a 1,3 matrix. How do you do it? Just multiply each entry in the first row of A by each entry in the first column of B and add the products. Do the same for the next row etc. Many (or should I honestly say MOST) people use their fingers and go along row one and then down column one. The add the products of the entries as they do that. Then they do the same for row two and column two etc. It really does help!
If properties of matrix addition let A B C D the m n matrix then 1A plus B B plus A?
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
Prove that a matrix which is both symmetric as well as skew symmetric is a null matrix?
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
Is Inverse of the inverse matrix the original 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.
Is an invertible idempotent matrix the identity matrix?
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
In the movie The Matrix what color pill?
blue
Let A be a 6by4 matrix and B a 4by6 matrix show that the 6by6 matrix AB can not be invertible?
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.
Is a singular matrix an indempotent matrix?
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!
Where may an individual find listings for properties to let?
Real Rentals is a good site one could visit to find listing of properties to let. Zoopla and Prime Locations also have good listings in the UK and allow one to search for properties to let by post code.
What are the properties of materials?
They don't let water through.
Heater matrix leaking on 1992 Ford Escort?
I'm doing mine Saturday, will let you know after
How do you do matrix operation in casio fx991ms?
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.
What element has properties of non metals and metals?
Mercury? its a liquid metal It has metal properties and liquid properties right? someone let me know.
