3.7 What are some of the rules of binary matrix operations?.3.6 What is a linear combination of matrices?.3.5 What is the scalar multiplication of a matrix?.2.16 What is the definition of the dot product of two vectors?.2.15 How can vectors be used to write simultaneous linear equations?.2.14 Prove that if the dimension of a set of vectors is less than the number of vectors in the set, then the set of vectors is linearly dependent.2.13 Prove that if a set of vectors is linearly dependent, then at least one vector can be written as a linear combination of others.2.12 Prove that if a set of m vectors is linearly independent, then a subset of the m vectors also has to be linearly independent.2.11 Prove that if a set of vectors contains the null vector, the set of vectors is linearly dependent.2.10 What do you mean by the rank of a set of vectors?.2.9 What do you mean by vectors being linearly independent?.2.8 What do you mean by a linear combination of vectors?.2.7 How do you multiply a vector by a scalar?.1.21 Consequences of diagonally dominant matrices.1.19 Irreducible diagonally dominant matrix.1.18 Strictly diagonally dominant matrix:.1.15 Do non-square matrices have diagonal entries?.1.4 What are the special types of matrices?.