Matrices

Question 1

What is a matrix?

Answer 1

A rectangular array of elements arranged in rows and columns to represent some specific information

Question 2

Describe how a matrix A with three rows and four columns is generalized

Answer 2

𝐴 = (𝑎𝑖𝑗) 𝑖[𝑟𝑜𝑤𝑠] = 1,2,3; 𝑗[𝑐𝑜𝑙𝑢𝑚𝑛𝑠] = 1,2,3,4

Question 3

Define Equal Matrices

Answer 3

Two matrices A and B are said to be equal if they have the same order and if aij=bij for every i and j. ie elements in the corresponding locations in the two matrices are the same

Question 4

Describe how a transpose of a matrix is obtained

Answer 4

A transpose of a matrix is obtained by interchanging the rows and columns of the given matrix

Question 5

Describe diagonal matrices

Answer 5

A matrix whose elements are 0 except for at least one element in the principal diagonal

Question 6

Describe an identity or unity matrix

Answer 6

A diagonal matrix in which all of the diagonal elements are positive one

Question 7

Describe a sub matrix

Answer 7

A matrix obtained by deleting row(s) and/or column(s) of a given matrix

Question 8

Describe a singular matrix

Answer 8

A matrix whose determinant is zero

Question 9

Define the inverse of a matrix

Answer 9

If A is a non-singular, square matrix and there exists another square matrix denoted by A-1 for which the product of A-1 and is an identity matrix, then A-1 is said to be the inverse of A and vice versa

Question 10

What is a matrix of minors

Answer 10

A matrix whose elements are the determinants of all 2*2 matrices obtained from a given matrix

Question 11

What is a cofactor matrix

Answer 11

A matrix whose elements are signed elements of the matrix of minors. The signs alternate both vertically and horizontally from + to - form m11