Solved Examples on Subtraction of Matrices

Example 1: Q1. Subtract the matrices: P = [Tex]\begin{bmatrix} 15 & 4\\13 & 9 \end{bmatrix}[/Tex] and Q = [Tex]\begin{bmatrix} 1 & -13\\ 6 & 0 \end{bmatrix}[/Tex]

Solution:

P – Q = [Tex]\begin{bmatrix} 15 & 4\\13 & 9 \end{bmatrix}[/Tex] – [Tex]\begin{bmatrix} 1 & -13\\ 6 & 0 \end{bmatrix}[/Tex]

P – Q = [Tex]\begin{bmatrix} 15-1 & 4-(-13)\\ 13- 6 & 9-0 \end{bmatrix}[/Tex]

P – Q = [Tex]\begin{bmatrix} 14 & 17\\7 & 9 \end{bmatrix}[/Tex]

Example 2: Subtract the matrices A = [Tex]\begin{bmatrix} -8& 3& 9\\ -1 & 2&6\\ 5& -12&4 \end{bmatrix}[/Tex] and B = [Tex]\begin{bmatrix} -3& 5& 13\\ -10 & 23&0\\ 7& -1&22 \end{bmatrix}[/Tex]

Solution:

A – B = [Tex]\begin{bmatrix} -8& 3& 9\\ -1 & 2&6\\ 5& -12&4 \end{bmatrix}[/Tex] – [Tex]\begin{bmatrix} -3& 5& 13\\ -10 & 23&0\\ 7& -1&22 \end{bmatrix}[/Tex]

A – B = [Tex]\begin{bmatrix} -8-( -3)& 3-5& 9-13\\ -1-(-10) & 2-23&6-0\\ 5-7& -12-(-1)&4 -22 \end{bmatrix} [/Tex]

A – B = [Tex]\begin{bmatrix} -5& -2& -4\\ 9 & -21&6\\ -2& -11& -18 \end{bmatrix}[/Tex]

Example 3: Compute R – S where R = [Tex]\begin{bmatrix} -2& 5& 1&10\\ -3 & 7&-1&8\\ 6& -10&0&-4 \end{bmatrix}[/Tex] and S = [Tex]\begin{bmatrix} 8& 4& -3&0\\ -5 & -2&7&12\\ 0& 1&-2&9 \end{bmatrix}[/Tex]

Solution:

R – S = [Tex]\begin{bmatrix} -2& 5& 1&10\\ -3 & 7&-1&8\\ 6& -10&0&-4 \end{bmatrix}[/Tex] – [Tex]\begin{bmatrix} 8& 4& -3&0\\ -5 & -2&7&12\\ 0& 1&-2&9 \end{bmatrix}[/Tex]

R – S = [Tex]\begin{bmatrix} -2-8& 5-4& 1-(-3)&10-0\\ -3-(-5) & 7-(-2)&-1-7&8-12\\ 6-0& -10-1&0-(-2)&4-9 \end{bmatrix} [/Tex]

R – S = [Tex]\begin{bmatrix} -10& 1& 4&10\\ 2 & 9&-8&-4\\ 6& -11&2&-5 \end{bmatrix}[/Tex]

Example 4: Subtract the matrices C = [Tex]\begin{bmatrix} -1& 3 \\ 0 & 2\\ \end{bmatrix}[/Tex] and D = [Tex]\begin{bmatrix} 1& 3& 2\\ 4 & 5&9\\ 6& 10&11 \end{bmatrix}[/Tex]

Solution:

Order of C = 2 × 2 and Order of D = 3 × 3

Order of C ≠ Order of D

So, subtraction cannot be performed in the given matrices as the order of the given matrices are different and subtraction can only be performed on order of same matrices.

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.”