Subtraction of n × n Matrices

The subtraction of n × n matrices include subtracting each row column (i, j) element of one matrix with corresponding row column (i, j) element of other matrix.

Consider matrix P = [Tex] \begin{bmatrix} p_{11} & p_{12}& … &p_{1n}\\ p_{21} & p_{22}&… & p_{2n}\\ .&.&…& .\\ .&.&…& .\\ p_{n1}&p_{n2}&…&p_{nn} \end{bmatrix} [/Tex] and Q = [Tex] \begin{bmatrix} q_{11} & q_{12}& … &q_{1n}\\ q_{21} & q_{22}&… & q_{2n}\\ .&.&…& .\\ .&.&…& .\\ q_{n1}&q_{n2}&…&q_{nn} \end{bmatrix} [/Tex]

P – Q = [Tex] \begin{bmatrix} p_{11}-q_{11} & p_{12}-q_{12}& … &p_{1n}-q_{1n}\\ p_{21}-q_{21} & p_{22}-q_{22}&… & p_{2n}-q_{2n}\\ .&.&…& .\\ .&.&…& .\\ p_{n1}-q_{n1}&p_{n2}-q_{n2}&…&p_{nn}-q_{nn} \end{bmatrix} [/Tex]

Subtraction of 2 × 2 Matrices

The subtraction of 2 × 2 matrices includes subtracting each row column (i, j) element of one matrix with corresponding row column (i, j) element of other matrix.

Consider matrix X = [Tex]\begin{bmatrix} x_{11} & x_{12}\\ x_{21} & x_{22} \end{bmatrix}[/Tex] and Y = [Tex]\begin{bmatrix} y_{11} & y_{12}\\ y_{21} & y_{22} \end{bmatrix}[/Tex]

X – Y = [Tex]\begin{bmatrix} x_{11}- y_{11}& x_{12} – y_{12}\\ x_{21}-y_{21} & x_{22} – y_{22} \end{bmatrix}[/Tex]

Subtraction of 3 × 3 Matrices

The subtraction of 3 × 3 matrices includes subtracting each row column (i, j) element of one matrix with corresponding row column (i, j) element of other matrix.

Consider matrix X = [Tex]\begin{bmatrix} x_{11} & x_{12}&x_{13}\\ x_{21} & x_{22}&x_{23}\\ x_{31} & x_{32}&x_{33} \end{bmatrix}[/Tex] and Y = [Tex]\begin{bmatrix} y_{11} & y_{12}&y_{13}\\ y_{21} & y_{22}&y_{23}\\ y_{21} & y_{22}&y_{23}\\ \end{bmatrix}[/Tex]

X – Y = [Tex]\begin{bmatrix} x_{11}- y_{11}& x_{12} – y_{12}& x_{13} – y_{13}\\ x_{21}-y_{21} & x_{22} – y_{22}& x_{23} – y_{23}\\ x_{31}-y_{31} & x_{32} – y_{32}& x_{33} – y_{33} \end{bmatrix}[/Tex]

Read More,

• Matrices
• Matrix Operations
• Types of Matrices
• Order of Matrix
• Matrix Multiplication

Subtraction of matrices is addition of the negative of a matrix to another matrix which means A – B = A + (-B). The subtraction of the matrix is subtracting the corresponding row-column element of one matrix with same row-column element of another matrix.

In this article we will explore subtraction of matrices in detail. We will also solve some examples related to subtraction of matrices. Let’s start our learning on the topic “Subtraction of Matrices.”