the matrix whose entries are all 0
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.
the transpose of null space of A is equal to orthogonal complement of A
yes, it is both symmetric as well as skew symmetric
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.