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
A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.A foreign can have null values and it can have duplicate values.
An idempotent matrix is a matrix which gives the same matrix if we multiply with the same. in simple words,square of the matrix is equal to the same matrix. if M is our matrix,then MM=M. then M is a idempotent matrix.
Reduced matrix is a matrix where the elements of the matrix is reduced by eliminating the elements in the row which its aim is to make an identity matrix.
If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
Yes.
Yes.
the matrix whose entries are all 0
there is none you weasel. the only good matrix is revolutions. :)
nullity of A is the dimension of null space of A.
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
A null matrix is a matrix with all its elements zero.EXAMPLES : (0 0) is a null row matrix.(0 0)(0 0) is a null square matrix.NOTE : Text handling limitations prevent the printing of large brackets to enclose the matrix array. Two pairs of smaller brackets have therefore been used.Answer 2:The above answer is a null matrix. However, the nullity of a matrix is the dimension of the kernel. Rank + Nullity = Dimension. So if you have a 4x4 matrix with rank of 2, the nullity must be 2. This nullity is the number of "free variables" you have. A 4x4 matrix is 4 simultaneous equations. If it is rank 2, you have only two independent equations and the other two are dependent. To solve a system of equations, you must have n independent equations for n variables. So the nullity tells you how short you are in terms of equations.
yes, it is both symmetric as well as skew symmetric
the transpose of null space of A is equal to orthogonal complement of A
No. A scalar matrix can not be a zero matrix Just a note on separate Qs & As here. I'd stumbled on this group because as I can't understand matrices, I wasn't looking deliberately, but it looks as if another questioner has also asked the same, albeit with the words reversed, and gained a "Yes" and explanation.
The only proper subset of a set comprising one element, is the null set.