Suggested languages for you:

Americas

Europe

Q2.

Expert-verifiedFound in: Page 163

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

**Give an example of two matrices whose sum is zero matrix.**

Two matrices whose sum is a zero matrix are $A=\left[\begin{array}{cc}2& -5\\ -1& 3\end{array}\right]$ and $B=\left[\begin{array}{cc}-2& 5\\ 1& -3\end{array}\right]$.** **

If A and B are two matrices of order $m\times n$, then the addition of the two matrices will also yield a matrix of order $m\times n$ wherein each element is the sum of the corresponding elements.

Write two matrices A and B such that the sum of the two matrices is zero. Note that since the sum has to be zero the order of both the matrices must be same. Consider the matrices of order $2\times 2$.

Let $A=\left[\begin{array}{cc}2& -5\\ -1& 3\end{array}\right]$ and $B=\left[\begin{array}{cc}-2& 5\\ 1& -3\end{array}\right]$.

Add the matrices A and B so as to verify if $A+B$ is a zero matrix. A zero matrix is a matrix whose each element is zero.

$\begin{array}{c}A+B=\left[\begin{array}{cc}2& -5\\ -1& 3\end{array}\right]+\left[\begin{array}{cc}-2& 5\\ 1& -3\end{array}\right]\\ =\left[\begin{array}{cc}2+\left(-2\right)& -5+5\\ -1+1& 3+\left(-3\right)\end{array}\right]\\ =\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]\end{array}$

94% of StudySmarter users get better grades.

Sign up for free