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Chapter 4: Q2. (page 163)

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

Short Answer

Expert verified

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

Step by step solution

01

- Define concept of matrix addition

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.

02

- Write two matrices

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 $A = [\begin{matrix} 2 & - 5 \\ - 1 & 3 \end{matrix}]$ and $B = [\begin{matrix} - 2 & 5 \\ 1 & - 3 \end{matrix}]$ .

03

- Verify

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.

$\begin{matrix} A + B = [\begin{matrix} 2 & - 5 \\ - 1 & 3 \end{matrix}] + [\begin{matrix} - 2 & 5 \\ 1 & - 3 \end{matrix}] \\ = [\begin{matrix} 2 + (- 2) & - 5 + 5 \\ - 1 + 1 & 3 + (- 3) \end{matrix}] \\ = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] \end{matrix}$

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Most popular questions from this chapter

Find the value of each expression.

52. $3.5 + 2.7$

Use matrices $A$ , $B$ , $C$ and $D$ to find the following.

$A = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}], B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], C = [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}], D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ - 3 & 0 \end{matrix}]$

27. $6 B - 2 A$

Find each product, if possible.

$[\begin{matrix} 7 & 3 \\ 0 & 2 \\ 5 & 5 \end{matrix}] \cdot [\begin{matrix} - 2 & 1 & 4 \\ 3 & - 5 & 2 \\ 4 & 3 & 1 \end{matrix}]$

Find each product, if possible.

$[\begin{matrix} 4 & - 2 & - 7 \\ 6 & 3 & 5 \end{matrix}] \cdot [\begin{matrix} - 2 \\ 5 \\ 3 \end{matrix}]$

Use matrices $A$ , $B$ , $C$ and $D$ to find the following.

$A = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}], B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], C = [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}], D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ - 3 & 0 \end{matrix}]$

24. $A + B$

See all solutions

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