nontrivial solution in homogeneous system means that the system has trivial solution in addition to infinitely many solutions

to say that A = B we have to achieve

The m x n matrix of all entries are equal to zero is called …

A + B = B + A

(A + B) + C = A + (B + C)

K(A + B) = KA + KB

A + 0 = 0 + A = A

A column vector

A row vector

in multiplying row vector by a column vector, they must have the same number of entries

A mxr . B rxn =

Cij =

to multiply two matrices A and B, (A.B) the number of columns of .. must be the equal the number of rows of …

Resulting matrix of multiplying A and B (A.B) has the same number of rows as .. and the same number of columns as ..

A.0 =

A.I =

I.A =

I^2 =

In general A.B = B.A

In matrices Multiplication is commutative

A.I = I.A = A