Students can Download Maths Chapter 4 Determinants Ex 4.4 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 4.4

### 2nd PUC Maths Determinants NCERT Text Book Questions and Answers Ex 4.4

Write the minors and co-factors of the elements of following determinants

Question 1.

(i)

\(\left|\begin{array}{cc}{2} & {-4} \\{0} & {3}\end{array}\right|\)

Answer:

(ii)

\(\left|\begin{array}{ll}{a} & {c} \\{b} & {d}\end{array}\right|\)

Answer:

Question 2

(i)

\(\left|\begin{array}{lll}{\mathbf{1}} & {\mathbf{0}} & {\mathbf{0}} \\{\mathbf{0}} & {\mathbf{1}} & {\mathbf{0}} \\{\mathbf{0}} & {\mathbf{0}} & {\mathbf{1}}\end{array}\right|\)

Answer:

(ii)

\(\left|\begin{array}{ccc}{1} & {0} & {4} \\{3} & {5} & {-1} \\{0} & {1} & {2}\end{array}\right|\)

Answer:

Question 3.

Using cofactors of elements of second row, Evaluate

\(\Delta\left|\begin{array}{lll}{1} & {0} & {0} \\{0} & {1} & {0} \\{0} & {0} & {1}\end{array}\right|\)

Answer:

C_{21} = 0 C_{22} = 1 C_{23 }= 0

∴ Δ A = 0 x 0 + 1 x 1 + 0 x 0 = 1

Question 4.

Using cofactors of elements of 3rd column

\(\Delta=\left|\begin{array}{lll}{\mathbf{1}} & {\mathbf{x}} & {\mathbf{y} \mathbf{z}} \\{\mathbf{1}} & {\mathbf{y}} & {\mathbf{z} \mathbf{x}} \\{\mathbf{1}} & {\mathbf{z}} & {\mathbf{x} \mathbf{y}}\end{array}\right|\)

Answer:

M_{13} = (z – y) M_{23} = (z-x) M_{33} = (y-x)

C_{13} = (z-y) C_{23} = -(z-n), C_{33} = (y – x)

Δ = yz (z – y) + zx{-(z – x)} + xy (y – x)

= yz^{2} – y^{2}z – z^{2}x + zx^{2} + xy^{2} – x^{2}y

x^{2} (z – y) + z (y^{2} – z^{2}) + yz (z – y)

x^{2} (z – y) + x (y+ z) (y- z) + yz (z – y)

(z – y) {x^{2} – x (y + z) + yz}

(z – y) {x^{2} – xy – xz + yz}

(z – y) {x (x – y) – z (x – y)}

(z – y) (x – y) (x – z) = (z – y) (y – x) (z – x)

Question 5.

\(\text { If } \Delta=\left|\begin{array}{lll}{\mathbf{a}_{11}} & {\mathbf{a}_{12}} & {\mathbf{a}_{13}} \\{\mathbf{a}_{21}} & {\mathbf{a}_{22}} & {\mathbf{a}_{23}} \\{\mathbf{a}_{31}} & {\mathbf{a}_{32}} & {\mathbf{a}_{33}}\end{array}\right|\) is a cofactors of a_{ij} then the calue of Δ is given by of

(A) a_{11} A_{31} + a_{12} A_{32} + a_{13} A_{33
}(B) a_{n} A_{n} + a_{12} A_{21} + a_{13} A_{31
}(C) a_{21} A_{u} + a_{22} A_{12} + a_{23} A_{13
}(D) a_{n} A_{n} + a_{21} A_{21} + a_{31} A_{31
}Answer:

Answer is (D)

i.e., a_{11} A_{11} + a_{21}+ a_{31} A_{31}