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## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2

**11th Maths Exercise 7.2 Question 1.**

Without expanding the determinant, prove that

Solution:

**11th Maths Exercise 7.2 Answers Question 2.**

Show that

Solution:

**Matrices And Determinants Class 11 Solutions Pdf Question 3.**

Prove that

Solution:

LHS

Taking a from C_{1}, b from C_{2} and c from C_{3} we get

Expanding along R_{1} we get

(2c) (abc) (1) [ab + ab] = abc (2c) (2ab)

1 = (abc) (4abc) = 4a^{2}b^{2}c^{2}

= RHS

**Matrices And Determinants Class 11 State Board Solutions Question 4.**

Solution:

**11th Maths Matrices And Determinants Solutions Question 5.**

Prove that

Solution:

**11th Maths Exercise 7.2 In Tamil Question 6.**

Show that

Solution:

**11th Maths Determinants Solutions Question 7.**

Write the general form of a 3 × 3 skew-symmetric matrix and prove that its determinant is 0.

Solution:

**11th Maths Exercise 7.2 Samacheer Kalvi Question 8.**

Solution:

we get – (aα^{2} + 2bα + c) [ac – b^{2}]

So Δ = 0 ⇒ (aα^{2} + 2bα + c) (ac -b^{2}) = – 0 = 0

⇒ aα^{2} + 2bα + c = 0 or ac – b^{2} = 0

(i.e.) a is a root of ax^{2} + 2bx + c = 0

or ac = b^{2}

⇒ a, b, c are in G.P.

**11th Maths Matrix Solutions Question 9.**

Prove that

Solution:

**Exercise 7.2 Class 11 Maths Solutions State Board Question 10.**

If a, b, c are p^{th}, q^{th} and r^{th} terms of an A.P., find the value of

Solution:

We are given a = t_{p},b = t_{q} and c = t_{r}

Let a be the first term and d be the common difference

**11th Maths Matrix And Determinants Question 11.**

Show that is divisible by x^{4}

Solution:

Multiplying R_{1} by a, R_{2} by b and R_{3} by c and

taking out a from C_{1} b from C_{2} and c from C_{3} we get

==

**11th Maths Ex 7.2 Question 12.**

If a, b, c are all positive, and are p^{th}, q^{th} and r^{th} terms of a G.P., show that

Solution:

**Exercise 7.2 Class 11 Maths Solutions Question 13.**

Find the value of if x, y, z ≠ 1.

Solution:

Expanding the determinant along R_{1}

**11th Std Maths Determinants Solutions Question 14.**

Solution:

**11th Maths Book Volume 2 Chapter 7 Question 15.**

Without expanding, evaluate the following determinants:

Solution:

**10th Maths Exercise 7.2 Samacheer Kalvi Question 16.**

If A is a square matrix and |A| = 2, find the value of |AA^{T}|.

Solution:

|A| = 2 (Given) |A^{T}| = 2

Now |AA^{T}| = |A| |A^{T}| = 2 × 2 = 4.

**12th Maths Exercise 7.2 Samacheer Kalvi Question 17.**

If A and B are square matrices of order 3 such that |A| = -1 and |B| = 3, find the value of |3AB|.

Solution:

Given |A| = -1 : |B| = 3

Given A and B are square matrices of order 3.

∴ |kAB| = k^{3} |AB|

Here k = 3 ∴ |3AB| = 3^{3} |AB|

= 27 |AB|

= 27 (-1) (3)

= -81

**Class 11 Maths Exercise 7.2 Solutions Question 18.**

If λ = -2, determine the value of

Solution:

Given λ = -2

∴ 2λ = -4; λ^{2} = (-2)^{2}; 3λ^{2} + 1 = 3 (4) + 1 = 13

6λ – 1 = 6(-2) – 1 = -13

expanding along R_{1}

0(0) + 4 (0 + 13) + 1 (-52 + 0) = 52 – 52 = 0

Aliter: The determinant value of a skew-symmetric matrix is zero

**Matrices And Determinants Class 11 Solutions Question 19.**

Determine the roots of the equation

Solution:

Given the determinant value is 0

⇒ 30(1 + x) (2 – x) = 0

⇒ 1 + x = 0 or 2 – x = 0

⇒ x = -1 or x = 2

So, x = -1 or 2.

**Matrices And Determinants Class 11 Exercise Question 20.**

Verify that det (AB) = (det A) (det B) for

Solution:

{(-20)(52) (-19) + (10)(38)(—49) + (2)(64)(-17)} – {(-49)(52) (2) + (-17)(38)(-20) + (-19)(64)(10)}

= (19760 – 18620 – 2176) – (-5096 + 12920 – 12160)

= (19760 + 5096 + 12160) – (18620 + 2176 + 12920)

= 37016 – 33716 = 3300 ….(3)

Now (1) × (2) = (3)

(i.e.,) (-33) (-100) = 3300

⇒ det (AB) = (det A), (det B)

**Determinants Class 11 State Board Solutions Question 21.**

Using cofactors of elements of second row, evaluate |A|, where

Solution:

### Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 Additional Problems

**Exercise 7.2 Class 10 Samacheer Kalvi Question 1.**

Solution:

**11th Maths Matrices And Determinants Pdf Question 2.**

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution: