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:

Question 2.

\(\left|\begin{array}{ccc}{1} & {-1} & {2} \\{2} & {3} & {5} \\{-2} & {0} & {1}\end{array}\right|\)

Answer:

Question 3.

Verify A(Adj A)=(adj A) A=|A| I

\(A=\left|\begin{array}{cc}{2} & {3} \\{-4} & {-6}\end{array}\right|\)

Answer:

Question 4.

\(\left|\begin{array}{ccc}{1} & {-1} & {2} \\{3} & {0} & {2} \\{1} & {0} &{2} \end{array}\right|\)

Answer:

Find the inverse of each of these matrices

Question 5.

\(\left[\begin{array}{cc}{2} & {-2} \\{4} & {3}\end{array}\right]\)

Answer:

Question 6.

\(A=\left[\begin{array}{ll}{-1} & {5} \\{-3} & {2}\end{array}\right]\)

Answer:

Question 7.

\(\left[\begin{array}{lll}{1} & {2} & {3} \\{0} & {2} & {4} \\{0} & {0} &{5}\end{array}\right]\)

Answer:

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:

Question 9.

\(\mathbf{A}=\left[\begin{array}{ccc}{2} & {1} & {3} \\{4} & {-1} & {0} \\{-7} & {2} & {1}\end{array}\right]\)

Answer:

Question 10.

\(\left[\begin{array}{ccc}{1} & {-1} & {2} \\{0} & {2} & {-3} \\{3} & {-2} &{4}\end{array}\right]\)

Answer:

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:

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:

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:

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

A^{1 }+ aA + bI = G,Ah. find A^{-1}

Answer:

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 A^{3 }+ 6A^{2} + 5A +11 I = 0

Answer:

Question 16.

\(\mathbf{A}=\left[\begin{array}{rrr}{2} & {-1} & {+1} \\{-1} & {2} & {-1} \\{1} & {-1} & {2}\end{array}\right]\),

verify that A^{3 }– 6A^{2} + 9A – 4I = 0. find A^{-1}

Answer:

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)

Question 18.

If A is an invertable matrix of oder 2, then det (A)^{-1}is equal to

(A) det A

(B)

(C) 0

(D) 1

Answer: