NCERT Solutions, Determinants, Part -5, Class 12, Maths, Notes - JEE

JEE: NCERT Solutions, Determinants, Part -5, Class 12, Maths, Notes - JEE

The document NCERT Solutions, Determinants, Part -5, Class 12, Maths, Notes - JEE is a part of JEE category.
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Determinants


Exercise 4.5


Question 1: Find adjoint of each of the matrices.

determinants, mathematics,Question and Answer (Q & A)


Answer

determinants, mathematics,Question and Answer (Q & A)

 


Question 2: Find adjoint of each of the matrices.

determinants, mathematics,Question and Answer (Q & A)


Answer

determinants, mathematics,Question and Answer (Q & A)

determinants, mathematics,Question and Answer (Q & A)



Question 3:
determinants, mathematics,Question and Answer (Q & A)


Answer

determinants, mathematics,Question and Answer (Q & A)

 

Question 4:
determinants, mathematics,Question and Answer (Q & A)


Answer

determinants, mathematics,Question and Answer (Q & A)

determinants, mathematics,Question and Answer (Q & A)

 

Question 5: Find the inverse of each of the matrices (if it exists).

Answer 5:

determinants,Class 11,CBSE,NCERT,Syllabus,Q and A,Important,Questions and Answers
determinants,Class 11,CBSE,NCERT,Syllabus,Q and A,Important,Questions and Answers


Question 6: Find the inverse of each of the matrices (if it exists).

determinants, mathematics,Question and Answer (Q & A)


Answer

determinants, mathematics,Question and Answer (Q & A)



Question 7: Find the inverse of each of the matrices (if it exists).

determinants, mathematics,Question and Answer (Q & A)


Answer

determinants, mathematics,Question and Answer (Q & A)

determinants, mathematics,Question and Answer (Q & A)


Question 8: Find the inverse of each of the matrices (if it exists).

determinants, mathematics,Question and Answer (Q & A)


Answer

determinants, mathematics,Question and Answer (Q & A)


Question 9: Find the inverse of each of the matrices (if it exists).

determinants, mathematics,Question and Answer (Q & A)


Answer

determinants, mathematics,Question and Answer (Q & A)


Question 10: Find the inverse of each of the matrices (if it exists).

determinants, mathematics,Question and Answer (Q & A)

Answer

determinants, mathematics,Question and Answer (Q & A)


Question 11: Find the inverse of each of the matrices (if it exists).

determinants, mathematics,Question and Answer (Q & A)

Answer

determinants, mathematics,Question and Answer (Q & A)


Question 12:
Let
determinants, mathematics,Question and Answer (Q & A) . Verify that (AB)-1 = B-1A-1


Answer

determinants, mathematics,Question and Answer (Q & A)

determinants, mathematics,Question and Answer (Q & A)

determinants, mathematics,Question and Answer (Q & A)

From (1) and (2), we have:
(AB)−1 = B−1A−1
Hence, the given result is proved.


Question 13:
If
determinants, mathematics,Question and Answer (Q & A) show that determinants, mathematics,Question and Answer (Q & A) Hence find A-1.


Answer

determinants, mathematics,Question and Answer (Q & A)

Question 14:
For the matrix determinants, mathematics,Question and Answer (Q & A) , find the numbers a and b such that A2 + aA + bI = O.


Answer


determinants, mathematics,Question and Answer (Q & A)
Hence, −4 and 1 are the required values of a and b respectively.


Question 15:
For the matrix
determinants, mathematics,Question and Answer (Q & A) show that A3 − 6A2 + 5A + 11 I = O. Hence, find
A−1.


Answer

determinants, mathematics,Question and Answer (Q & A)

determinants, mathematics,Question and Answer (Q & A)
determinants, mathematics,Question and Answer (Q & A)


Question 16:
If
determinants, mathematics,Question and Answer (Q & A)  verify that A3 − 6A2 + 9A − 4I = O and hence find A−1


Answer

determinants, mathematics,Question and Answer (Q & A)

determinants, mathematics,Question and Answer (Q & A) determinants, mathematics,Question and Answer (Q & A)


From equation (1), we have:

determinants, mathematics,Question and Answer (Q & A)


Question 17:
determinants, mathematics,Question and Answer (Q & A)


Answer B
determinants, mathematics,Question and Answer (Q & A)
Hence, the correct answer is B.


Question 18: If A is an invertible matrix of order 2, then det (A−1) is equal to determinants, mathematics,Question and Answer (Q & A)


Answer
B. C. D.

determinants, mathematics,Question and Answer (Q & A)
Hence, the correct answer is B.

The document NCERT Solutions, Determinants, Part -5, Class 12, Maths, Notes - JEE is a part of JEE category.
All you need of JEE at this link: JEE

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