ICSE Class X Math 2016 Solved Paper

Given A=[
4sin‌30∘ cos‌0∘
cos‌0∘ 4sin‌30∘
] and B=[
4
5
] If AX=B

Question : 28

Total: 57

Find the matrix X.

Solution:

Let X=[

]
∴[

4sin‌30∘	cos‌0∘
cos‌0∘	4sin‌30∘

][

] =[

]
⇒‌‌[

4asin‌30∘+b‌cos‌0∘

a‌cos‌0∘+4bsin‌30∘

] =[

]
⇒‌‌4asin‌30∘+b‌cos‌0∘=4
⇒‌‌4a×‌

+b×1=4
⇒‌‌2a+b=4 ........(1)
and ‌‌a‌cos‌0∘+4bsin‌30∘=5
⇒9×1+4b×‌

‌=5
⇒‌a+2b‌=5. ...........(2)
Solving eqs (1) & (2), we get
a=1‌ and ‌b=2
Hence X=[

]

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