Math, asked by muzugj, 7 months ago

If A and B are 2 x 2 diagonal matrices, then A + B is a 2 x 2 diagonal matrix.​

Answers

Answered by syed2020ashaels
2

Answer:

yes , statement is correct

Step-by-step explanation:

A and B are 2×2 diagonal matrix

i.e. take a example

 a \:  = \binom{1 \:  \: 2}{3 \:  \: 4}  \:  \: b =  \binom{1 \:  \: 0}{0 \:  \: 1}

then we apply multiplication rule ,

 a \times b = \binom{1 \times 1 + 2 \times 0 \:  \:  \:  \: 1 \times 0 + 2 \times 1}{3 \times 1  + 4 \times 0 \:  \:  \:  \: 3 \times 0 + 4 \times 1}

 a \times b \:  = \binom{1 \:  \: 2}{3 \:  \: 4}

Here the a and b matrix are of 2×2 matrix then it gives the 2×2 matrix but it changes according to the i×j matrix

similarly ,

a + b \:  =  \binom{1 + 1 \:  \: 2 + 0}{3 + 0 \:  \: 4 + 1}

 a + b = \binom{2 \:  \: 2}{3 \:  \: 5}

Here in Addition matrix there is compulsory to be same matrix in both a and b . If this not given in same matrix then we can't apply addition rule on matrix.

#SPJ2

Similar questions