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NCERT Class 12- Mathematics: Exemplar Chapter β 3 Matrices Part 9
Question 20:
If , then find a non-zero matrix C such that .
Answer:
We have,
Let is a non-zero matrix of order .
And
For
On using equality of matrix, we get
We see that on taking C of order We get
In general,
Where, is any real number.
Question 21:
Give an example of matrices A, B and C such that , where A is nonzero matrix, but .
Answer:
Thus, we see that [using Eq. (i) and (ii) ]
Where, A is non-zero matrix but .
Question 22:
If
(i)
(ii) .
Answer:
We have,
(i)
And
Again,
[using Eq. (i) and (ii) ]
(ii)
And
Also
And
From Eq. (iii) and (iv) ,
Question 23:
If prove that
Answer:
And
Thus, we see that, [using Eq. (i) and (ii) ]
Hence Proved.