Matrices

# Terms and definitions:

### Matrix: A rectangular arrangement of mn elements in the form of an ordered set of m rows, each row consisting of an ordered set of n elements is called m x n matrix.

### Types of Matrices

Row matrix: A matrix having only one row

Column matrix: A matrix having only one column

Zero/Null matrix: Matrix whose all elements are zero

Square matrix: A matrix whose number of rows and columns are equal

Diagonal matrix: A square matrix whose non-diagonal elements are always zero

Scalar matrix: A Diagonal matrix in which all the diagonals are equal and non-diagonal elements are zero

Identity/Unit matrix: A scalar matrix where all diagonal elements are 1 and non-diagonal elements are zero

Triangular matrix: A square matrix where all elements towards either side (upper or lower) are zero

# Practice Questions:

**Question:** Let A = [ 3 7 -1 || 0 2 5 ] and B = [ 7 9 0 || 3 -5 6]. Find the sum of (2,2) entries of A and B. **Answer:** - 3

**Question:** Find the value of x - y + z if [ x+y+z || x+z || y+z ] = [ 9 5 7 ]. **Answer:** 1

# Matrices

# Terms and definitions:

### Matrix: A rectangular arrangement of mn elements in the form of an ordered set of m rows, each row consisting of an ordered set of n elements is called m x n matrix.

### Types of Matrices

Row matrix: A matrix having only one row

Column matrix: A matrix having only one column

Zero/Null matrix: Matrix whose all elements are zero

Square matrix: A matrix whose number of rows and columns are equal

Diagonal matrix: A square matrix whose non-diagonal elements are always zero

Scalar matrix: A Diagonal matrix in which all the diagonals are equal and non-diagonal elements are zero

Identity/Unit matrix: A scalar matrix where all diagonal elements are 1 and non-diagonal elements are zero

Triangular matrix: A square matrix where all elements towards either side (upper or lower) are zero

# Practice Questions:

**Question:** Let A = [ 3 7 -1 || 0 2 5 ] and B = [ 7 9 0 || 3 -5 6]. Find the sum of (2,2) entries of A and B. **Answer:** - 3

**Question:** Find the value of x - y + z if [ x+y+z || x+z || y+z ] = [ 9 5 7 ]. **Answer:** 1