NCERT Class 12-Mathematics: Exemplar Chapter – 4 Determinants Part 3 (For CBSE, ICSE, IAS, NET, NRA 2023)
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Question 5:
If , then show that is equal to zero.
Answer:
Interchanging rows and columns, we get
Taking ′ common from and , we get
Question 6:
Prove that , where A is an invertible matrix.
Answer:
Since A is an invertible matrix, so it is non-singular.
We know that . But . So i.e.. is invertible matrix.
Now we know that .
Taking transpose on both sides, we get
Hence is inverse of , i.e.. ,
Long Answer (L. A.)
Question 7:
If is a root of , then find the other two roots
Answer:
Applying , we get
Taking common from , we get
Applying , we get
Expanding along ,
. Thus, implies
Question 8:
In a triangle , if
then prove that is an isosceles triangle.
Answer:
Expanding along , we get
triangle ABC is isoceles.
Question 9:
Show that if the determinant then
Answer:
we get
or
or
or
or
or (Why?) .