NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev

The document NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
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DETERMINANTS

Exercise 4.4

Question 1:

Write Minors and Cofactors of the elements of following determinants:
 (i) 
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev
Answer
(i) The given determinant is NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev

Minor of element aij is Mij.
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev


NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev


Question 2:
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev
Answer
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev


NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev


Question 3: Using Cofactors of elements of second row, evaluate Δ =
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev.


Answer
The given determinant is
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev .
We have:
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev

NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev

NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev

We know that ∆ is equal to the sum of the product of the elements of the second row with their corresponding cofactors. 

∆ = a21A21 + a22A22 + a23A23 = 2(7) + 0(7) + 1(−7) = 14 − 7 = 7 

Question 4: Using Cofactors of elements of third column, evaluate Δ=  

NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev


Answer
The given determinant is NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev .
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev
We know that Δ is equal to the sum of the product of the elements of the second row
with their corresponding cofactors.

NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev

Hence,


Question 5: For the matrices A and B, verify that (AB)′ = B'A' where
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev


Answer
NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev

NCERT Solutions - Determinants, Exercise 4.4 JEE Notes | EduRev
Hence,

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