Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices are part of Plus Two Maths Chapter Wise Questions and Answers. Here we have given Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus Two |

Subject | Maths Chapter Wise Questions |

Chapter | Chapter 3 |

Chapter Name | Matrices |

Number of Questions Solved | 39 |

Category | Plus Two Kerala |

## Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices

**Short Answer Type Questions**

**(Score 3)**

Question 1.

Find the inverse of the matrix

using column transformation.

Answer.

A = I A. For column transformation

Question 2.

i. Find AB.

ii. If C is the matrix obtained from A by the transformation R1 → 2R1 , find CB.

Answer.

Question 3.

If

(i) Find A² and 4A.

(ii) If f (x) = x² + 4x – 5, find f (A)

Answer.

Question 4.

The co-operative store of a particular school has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are Rs 65.70, Rs 43.20 and Rs 76.50 respectively. Find by matrix method, the total amount of the store will receive from selling all these items.

Answer.

[Total cost] =

= [120 × 65.70 + 96 × 43.20 + 60 × 76.50] = [16621.20]

Total amount = Rs 16621.20

Question 5.

a. If the A.n is equal to -1

b. Find the values of x, y, z respectively if,

Answer.

Question 6.

Find the value of a,b,c and d from the equation :

Answer.

Equating the corresponding elements of the two matrices, we get

a-b = -1 ……(1)

2a+c = 5 …..(2)

2a-b = 0 …… (3)

3c+d = 13 ……(4)

(3)-(1) ⇒a = 1

(4) ⇒c = 3

(3) ⇒b = 2

(4) ⇒d = 4

Question 7.

Compute the following

Answer.

Question 8.

If

i. Find A+B

ii. Find (A+B)C.

Answer.

i. A and B are of the same order

ii. A+B and C are conformable for multiplication.

Question 9.

Using elementary row transformations, find the inverse of the matrix,if it exits

Answer.

Let

To use elementary row transformations, write A = IA

Question 10.

If is such that A² = I, then prove that 1 – α² – βγ = 0

Answer.

A² = I

**Long Answer Type Questions**

**(Score 4)**

Question 1.

Consider the matrix

A =

i. Find A + A^{T} and show that it is symmetric.

ii. Find A – A^{T} and show that it is skew symmetric.

iii. Express A as the sum of a symmetric and skew-symmetric matrices.

Answer.

Where the first matrix on the RHS is symmetric and the second one is skew symmetric.

Question 2.

Use matrix multiplication to divide Rs 30,000 in two parts such that the total annual interest at 9% on the first part and at 11% on the second part amounts to Rs 3060.

Answer.

Let the parts be x and (30000 – x)

Question 3.

If

(i) If ( A + B)² = A² + B², Prove that BA + AB = 0.

(ii) Find a and b.

Answer.

(i) (A + B)² = A² + B²

(A + B)(A + B) = A² + B²

(A + B)A + (A + B)B = A² + B²

A² + BA + AB + B² = A² + B²

BA + AB = 0

Question 4.

If A = and B = [-2 -1 – 4]

(i) Find out the product AB.

(ii) Find A^{T} and B^{T}.

(iii) Verify that (AB)^{T} = B^{T}.A^{T}

Answer.

Question 5.

Consider the matrices

(i) Find AB

(ii) Find the value of x such that ABC = 0.

Answer.

Question 6.

Let A is a third order square matrix given by

(i) Construct the matrix A.

(ii) Interpret the matrix A.

(iii) If B = then find AB – BA.

(iv) Interpret AB – BA.

Answer.

Question 7.

Find the inverse of matrices

Answer.

let A =

Write A = IA

Question 8.

If then prove that , where n is any positive integer.

Answer.

P(k+1) is true, whenever P(k) is true.

Hence by the principle of Mathematical

Induction P(n) is true for all n ∈ N.

Question 9.

For what values of x:

Answer.

Question 10.

Using elementary row transformations, find the inverse of the matrix if it exists.

Answer.

To use elementary row transformations,write A = IA.

A^{-1} does not exist. Since the elements of second row of the matrix on LHS are zero.

**Very Long Answer Type Questions**

**(Score 6)**

Question 1.

Let A =

(i) Find out I + A and I – A.

(ii) Show that

Answer.

Let tanx/2 = t

Question 2.

Let A is a third order square matrix given by

(i) Construct the matrix A.

(ii) Interpret the matrix A.

(iii) If B = then find AB – BA.

(iv) Interpret AB – BA.

Answer.

Question 3.

If

(i) Find the order of matrix A.

(ii) Find the matrix A, using the idea of equality of matrices.

Answer.

i. Clearly the product is a 3 x 3 matrix and the pre-factor is a 3 x 2 matrix. So A must be a 2 x 3 matrix.

Question 4.

a. Find the inverse of A = by using elementary operations.

b. Solve: sin^{-1} (1 – x) – 2sin^{-1} x =

Answer.

Question 5.

Find the Matrix X so that

Answer.

It is clear that the order of X is 2 x 2.

Since the product exists. Let

Then

**Edumate Questions & Answers**

Question 1.

If

, then find the values of x,y and z.

Answer.

z = 3

– y + z = 5 ⇒ y = z – 5 = 3 – 5 = – 2

x – y + = 0 ⇒ x = y – z = – 2 + 3, z = 1

Question 2.

i. If B = find B²

ii. If A = find A² is the identify matrix, then find x.

Answer.

Question 3.

Let the order of a matrix A is 2×3, order of a matrix B is 3×2 and order of matrix C is 3×3, then match the following

Answer.

i. Order of matrix CB is 3×2

ii. Order of matrix AC is 2×3

iii. Order of matrix BAC is 3×3

Question 4.

Answer.

Question 5.

Choose the correct answer from the bracket

i. If A = [a_{ij}]_{2×2} where a_{ij} = i + j, then A is equal to

a. Symmetric matrix

b. Skew-symmetric matrix

c. null matrix

d. Identity matrix

a. A symmetric matrix

b. a skew -symmetric matrix

c. a unit matrix

d. a null matrix

Answer.

i. A = a_{11} = 1 + 1 = 2,

a_{12} = 1 + 2 + 3, a_{21} = 2 + 1 = 3

Question 6.

Let A and B be two symmetric matrices of same order. Then show that AB-BA is a skew-symmetric matrix

Answer.

i. Given A = A^{T}, B = B^{T}

(AB – BA)^{T} = (AB)^{T}-(BA)^{T}

=B^{T}A^{T}-A^{T}B^{T} = BA-AB = -(AB-BA)

Therefore AB-BA is skew-symmetric matrix

Question 32.

then

i. Find 4A and A²

ii. Show that A²-4A = 5I_{3}

Answer.

Question 7.

ii. If the product AB is null matrix, then show that α – β is a multiple of

Answer.

Question 8.

Let A =

i. Find A².

ii. If A^{4} = I_{2,} then show that ab = 1

Answer.

Question 9.

Of the matrices A = and B =

i. Find AB, B^{T}, (AB)^{T}

ii. Show that (AB)^{T} = B^{T}A^{T}

Answer.

**NCERT Questions & Answers**

Question 1.

a. If a matrix has 5 elements, write all possible orders it can have.

b. Consider the matrix A =

(i) Express the matrix as A = IA

(ii) Find A^{-1} using elementary row transformations.

Answer.

a. Given that matrix has 5 elements.

So that possible orders are 1×5 or 5×1

Question 2.

positive integer n.

(i) Show that result is true for n = 1

(ii) Show that lithe result ¡s true for n = m, it is true for n = m + 1 also.

Answer.

(i) When n = 1

This shows that the result is true for n = m + 1 whenever it is true for n = m. Hence the result is true for any positive integer.

Question 3.

Answer.

This shows that the result is true for n = m + 1, whenever it is true for n = m. Hence by principle of mathematical induction, it is true for all n ∈ N.

Question 4.

If

(i) Find F(x +y).

(ii) Find F(x). F(y)

(iii) Is F(x). F(y) = F(x + y)?

Answer.

(i) F(x+y) =

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