2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5

Students can Download Maths Chapter 4 Determinants Ex 4.5 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5

2nd PUC Maths Determinants NCERT Text Book Questions and Answers Ex 4.5

Find the adjoint of each of the matrices

Question 1.
\(\left|\begin{array}{ll}{1} & {2} \\{3} & {4}\end{array}\right|\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.1

Question 2.
\(\left|\begin{array}{ccc}{1} & {-1} & {2} \\{2} & {3} & {5} \\{-2} & {0} & {1}\end{array}\right|\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.2

KSEEB Solutions

Question 3.
Verify A(Adj A)=(adj A) A=|A| I
\(A=\left|\begin{array}{cc}{2} & {3} \\{-4} & {-6}\end{array}\right|\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.3

Question 4.
\(\left|\begin{array}{ccc}{1} & {-1} & {2} \\{3} & {0} & {2} \\{1} & {0} &{2} \end{array}\right|\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.4
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.5

KSEEB Solutions

Find the inverse of each of these matrices

Question 5.
\(\left[\begin{array}{cc}{2} & {-2} \\{4} & {3}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.6

Question 6.
\(A=\left[\begin{array}{ll}{-1} & {5} \\{-3} & {2}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.7

Question 7.
\(\left[\begin{array}{lll}{1} & {2} & {3} \\{0} & {2} & {4} \\{0} & {0} &{5}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.8
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.9

KSEEB Solutions

Question 8.
\(\mathbf{A}=\left[\begin{array}{ccc}{\mathbf{1}} & {\mathbf{0}} &{\mathbf{0}} \\{\mathbf{5}} & {\mathbf{3}} & {\mathbf{0}} \\{\mathbf{5}} &{\mathbf{2}} & {-\mathbf{1}}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.10

Question 9.
\(\mathbf{A}=\left[\begin{array}{ccc}{2} & {1} & {3} \\{4} & {-1} & {0} \\{-7} & {2} & {1}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.11

Question 10.
\(\left[\begin{array}{ccc}{1} & {-1} & {2} \\{0} & {2} & {-3} \\{3} & {-2} &{4}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.12
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.13

Question 11.
\(\mathbf{A}=\left[\begin{array}{cccc}{\mathbf{1}} & {\mathbf{0}} & {} & {\mathbf{0}} \\{\mathbf{0}} & {\cos \theta} & {\sin \theta} \\{\mathbf{3}} & {\sin \theta} & {-\cos \theta}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.14

KSEEB Solutions

Question 12.
\(\begin{aligned}&\text { Let } A=\left[\begin{array}{ll}{3} & {7} \\{2} &{5}\end{array}\right], B=\left[\begin{array}{ll}{6} & {8} \\{7} & {9}\end{array}\right]\\&\text { verify }(A B)^{-1}=B^{-1} A^{-1}\end{aligned}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.15
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.16

Question 13.
\(\text { If } A=\left[\begin{array}{cc}{3} & {1} \\{-1} & {2}\end{array}\right]\) show that A – 5A +7I = 0 hence find A-1
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.17

KSEEB Solutions

Question 14.
Find the matrices \(\mathbf{A}=\left[\begin{array}{ll}{\mathbf{3}} & {\mathbf{2}} \\{\mathbf{1}} & {\mathbf{1}}\end{array}\right]\), find the numbers a and b such that
A1 + aA + bI = G,Ah. find A-1
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.18
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.19

Question 15.
For the matrix
\(\mathbf{A}=\left[\begin{array}{ccc}{\mathbf{1}} & {\mathbf{1}} & {\mathbf{1}} \\{\mathbf{1}} & {\mathbf{2}} & {-\mathbf{3}} \\{\mathbf{2}} & {-\mathbf{1}} & {\mathbf{3}}\end{array}\right]\)
show that A3 + 6A2 + 5A +11 I = 0
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.20
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.21

KSEEB Solutions

Question 16.
\(\mathbf{A}=\left[\begin{array}{rrr}{2} & {-1} & {+1} \\{-1} & {2} & {-1} \\{1} & {-1} & {2}\end{array}\right]\),
verify that A3 – 6A2 + 9A – 4I = 0. find A-1
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.22
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.23

Question 17.
Let A be a non singular matrix of order 3 x 3 then|Adj A| is equals to
(A) |A|
(B) |A|2
(C) |A|3
(D) 3|A|
Answer:
|Adj A| = |A|n – 1
hence the order is 3
|Adj A| = |A|3 – 1 |A|2
∴The correct answer is (B)

KSEEB Solutions

Question 18.
If A is an invertable matrix of oder 2, then det (A)-1is equal to
(A) det A
(B)
(C) 0
(D) 1
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.5.24