Question

Solve the addition matrix : - ​

Answer 1

This Is your Answer



$\mathbf{\[ \left[ {\begin{array}{cc} 2a& 0 \\ 0 & 2a \\ \end{array} } \right] \]}$

Answer 2

Question : -

Solve the addition matrix : -

$\left[\begin{array}{cc}a&-b\\b&a\end{array}\right] + \: \left[\begin{array}{cc}a&b \\-b&a \end{array}\right]$

Answer : -

$\left[\begin{array}{cc}2a&0 \\ 0&2a \end{array} \right]$

Step-by-step explanation : -

As we know,

Matrix is the rearranging of numbers.

Here, in this addition matrix, we have to add the like terms. Like terms are the terms which are similar.

For example : - 2a, 3a, 4a, and so on.

Here, we are gonna to add like terms.

But before we go on, let's learn some rules of negative and positive sign's addition.

(i) (+) + (+) = (+)

Example : - 8 + 2 = 10

(ii) (-) + (-) = (-)

Example : - - 8 + (-2) = - 10

(iii) (+) + (-) = greater number's sign

Example : - - 8 + 2 = 10

(iv) (-) + (+) = greater number's sign

Example : - 8 - 2 = 6

Now, we have learnt 'bout the sign rules. Now, we'll add the above matrix by using this formula.

$\left[\begin{array}{cc}a&-b\\b&a\end{array}\right] + \left[\begin{array}{cc}a&b \\-b&a \end{array}\right]$

Now add the like terms as following : -

(i) (a) + (a) = 2a

[(+) + (+) = (+)]

(ii) (-b) + (b) = 0

[(-) + (+) = greater number's sign]

(iii) (b) + (-b) = 0

[(+) + (-) = greater number's sign]

(iv) (a) + (a) = 2a

[(+) + (+) = (+)]

So, our answer will be,

$\left[\begin{array}{cc}2a&0 \\ 0&2a \end{array}\right]$