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Solution - if  A=[[2,0,0],[0,2,0],[0,0,2]] then A^6 - Operations on Matrices - Addition of Matrices

Question

if  `A=[[2,0,0],[0,2,0],[0,0,2]]` then A6=  ......................

(a) 6A

(b) 12A

(c) 16A

(d) 32A

 

Solution

i. (d)

Given that

`A=[[2,0,0],[0,2,0],[0,0,2]]`

we can write 

`A=2[[1,0,0],[0,1,0],[0,0,1]]`

Here 2 is scalar multiple

Terefore ,A=2 x I, where I= `[[1,0,0],[0,1,0],[0,0,1]]`

thus ,`A^6={2[[1,0,0],[0,1,0],[0,0,1]]}^6`

`            =2^6xx[[1,0,0],[0,1,0],[0,0,1]]^6`

`=2^6xxI^6,`

=26 x I,since I6=I

=2 5 x A [ A=2I]

=32A

 

 

Is there an error in this question or solution?

APPEARS IN

2014-2015 (March)
Question 1.1.1 | 2 marks
Solution for question: if  A=[[2,0,0],[0,2,0],[0,0,2]] then A^6 concept: Operations on Matrices - Addition of Matrices. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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