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SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 1 - Matrics [Latest edition]

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12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 - Shaalaa.com
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Chapter 1: Matrics

MCQVery Short AnswerShort Answers IShort Answers IILong Answers III
MCQ

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics MCQ

2 marks

MCQ | Q 1

The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is 

  • `[(4, 8, 3),(2, 1,6),(0, 2, 1)]`

  • `[(1, -1, 0),(-2, 3, -4),(-2, 3, -3)]`

  • `[(11, 9, 3),(1, 2, 8),(6, 9, 1)]`

  • `[(1, -2, 1),(-1, 3, 3),(-2, 3, -3)]`

MCQ | Q 2

A = `[(cos alpha, - sin alpha,  0),(sin alpha, cos alpha,  0),(0, 0, 1)]`, then A−1 is

  • A

  • − A

  • adj (A)

  • − adj (A)

MCQ | Q 3

The solution (x, y, z) of the equation `[(1, 0, 1),(-1, 1, 0),(0, -1, 1)] [(x),(y),(z)] = [(1),(1),(2)]` is (x, y, z) =

  • (1, 1, 1)

  • (0, −1, 2)

  • (−1, 2, 2)

  • (−1, 0, 2)

MCQ | Q 4

If ω is a complex cube root of unity, then the matrix A = `[(1, ω^2, ω),(ω^2, ω, 1),(ω, 1, ω^2)]` is

  • Singular matrix

  • Non−symmetric matrix

  • Skew−symmetric matrix

  • Non−Singular matrix

MCQ | Q 5

If A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______

  • 1

  • 3

  • 2

  • 4

MCQ | Q 6

`cos theta [(cos theta, sin theta),(-sin theta, cos  theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______

  • `[(0, 0),(0, 0)]`

  • `[(0, 1),(1, 0)]`

  • `[(1, 0),(0, 0)]`

  • `[(1, 0),(0, 1)]`

MCQ | Q 7

If A = `[(0, 0, -1),(0, -1, 0),(-1, 0, 0)]`, then the only correct statement about the matrix A is ______

  • A2 = I

  • A is a zero matrix

  • A−1 does not exit

  • A = (−1) I, where I is a unit matrix

MCQ | Q 8

If A = `[(cos alpha, sin alpha),(-sin alpha, cos 10 alpha)]`, then A10 = ______

  • `[(cos10  alpha, -sin10  alpha),(sin10  alpha, cos10  alpha)]`

  • `[(cos10  alpha, sin10  alpha),(-sin10  alpha, cos10  alpha)]`

  • `[(cos10  alpha, sin10  alpha),(-sin10  alpha, -cos10  alpha)]`

  • `[(cos10  alpha, -sin10  alpha),(-sin10  alpha, -cos10  alpha)]`

MCQ | Q 9

The element of second row and third column in the inverse of `[(1, 2, 1),(2, 1, 0),(-1, 0, 1)]` is ______

  • −2

  • −1

  • 1

  • 2

MCQ | Q 10

If A = `[(4, 5),(2, 5)]`, then |(2A)−1| = ______

  • `1/30`

  • `1/20`

  • `1/60`

  • `1/40`

MCQ | Q 11

If `[(x - y - z),(-y + z),(z)] = [(0),(5),(3)]`, then the value of x, y and z are respectively ______

  • 0, −3, 3

  • 1, −2, 3

  • 5, 2, 2

  • 11, 8, 3

MCQ | Q 12

The value of x, y, z for the following system of equations x + y + z = 6, x − y+ 2z = 5, 2x + y − z = 1 are ______

  • x = 1, y = 2, z = 3

  • x = 2, y = 1, z = 3

  • x = −1, y = 2, z = 3

  • x = y = z = 3

MCQ | Q 13

If A = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then |A| |adj A| = ______

  • 33

  • 39 

  • 36

  • 327

MCQ | Q 14

System of equations x + y = 2, 2x + 2y = 3 has ______

  • no solution

  • only one solution

  • many finite solutions.

  • infinite solutions.

MCQ | Q 15

If A = `[(1, -1, 1),(2, 1, -3),(1, 1, 1)]`, 10B = `[(4, 2,2),(-5, 0, ∞),(1, -2, 3)]` and B is the inverse of matrix A, then α = ______

  • –2

  • –1

  • 2

  • 5

Very Short Answer

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics Very Short Answer

1 Mark

Very Short Answer | Q 1

If A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find the value of a31A31 + a32A32 + a33A33 

Very Short Answer | Q 2

For an invertible matrix A, if A . (adjA) = `[(10, 0),(0, 10)]`, then find the value of |A|

Very Short Answer | Q 3

If the inverse of the matrix `[(alpha, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exists then find the value of α

Very Short Answer | Q 4

If A = `[(2, 2),(-3, 2)]` and B = `[(0, -1),(1, 0)]`, then find the matrix (B−1 A−1)−1 

Very Short Answer | Q 5

A = `[(cos theta, - sin theta),(-sin theta, -cos theta)]` then find A−1 

Very Short Answer | Q 6

If A = `[("a", "b"),("c", "d")]` then find the value of |A|−1 

Very Short Answer | Q 7

If A = `[(3, 1),(5, 2)]`, and AB = BA = I, then find the matrix B

Very Short Answer | Q 8

If A(α) = `[(cos alpha, sin alpha),(-sin alpha, cos alpha)]` then prove that A2(α) = A(2α)

Very Short Answer | Q 9

If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB

Very Short Answer | Q 10

A + I = `[(3, -2),(4, 1)]` then find the value of (A + I)(A − I)

Very Short Answer | Q 11

If A = `[(2, -1, 1),(-2, 3, -2),(-4, 4, -3)]` the find A2 

Very Short Answer | Q 12

If A = `[(-2, 4),(-1, 2)]` then find A2 

Very Short Answer | Q 13

If A = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)]` and B = `[(x),(y),(z)]`, find the matrix B'(AB)

Short Answers I

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics Short Answers I

2 Marks

Short Answers I | Q 1

If f(x) = x2 − 2x − 3 then find f(A) when A = `[(1, 2),(2, 1)]`

Short Answers I | Q 2

If A = `[(-1),(2),(3)]`, B = `[(3, 1, -2)]`, find B'A'

Short Answers I | Q 3

If A is invertible matrix of order 3 and |A| = 5, then find |adj A|

Short Answers I | Q 4

If A = `[(6, 5),(5, 6)]` and B = `[(11, 0),(0, 11)]` then find A'B'

Short Answers I | Q 5

If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A−1 B−1)

Short Answers I | Q 6

If A = `[(2,0),(0, 1)]` and B = `[(1),(2)]` then find the matrix 𝑋 such that A−1 X = B

Short Answers I | Q 7

Find the matrix X such that AX = I where A = `[(6, 17),(1, 3)]`

Short Answers I | Q 8

Find A–1 using adjoint method, where A = `[(cos theta, sin theta),(-sin theta, cos theta)]`

Short Answers I | Q 9.1

Find A−1 using column transformations:

A = `[(5, 3),(3, -2)]`

Short Answers I | Q 9.2

Find A−1 using column transformations:

A = `[(2, -3),(-1, 2)]`

Short Answers I | Q 10

Find the adjoint of matrix A = `[(6, 5),(3, 4)]`

Short Answers I | Q 11

Transform `[(1, 2, 4),(3, -1, 5),(2, 4, 6)]` into an upper triangular matrix by using suitable row transformations

Short Answers II

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics Short Answers II

3 Marks

Short Answers II | Q 1

If A = `[(0, 4, 3),(1, -3, -3),(-1, 4, 4)]`, then find A2 and hence find A−1 

Short Answers II | Q 2

If A = `[(0, 1),(2, 3),(1, -1)]` and B = `[(1, 2, 1),(2, 1, 0)]`, then find (AB)−1 

Short Answers II | Q 3

If A = `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`, find adj (A)

Short Answers II | Q 4

Solve the following by inversion method 2x + y = 5, 3x + 5y = −3

Short Answers II | Q 5

If A = `[(1, 2, -1),(3, -2, 5)]`, apply R1 ↔ R2 and then C1 → C1 + 2C3 on A

Short Answers II | Q 6

Three chairs and two tables cost ₹ 1850. Five chairs and three tables cost ₹2850. Find the cost of four chairs and one table by using matrices

Short Answers II | Q 7

If A = `[(4,5),(2,1)]`, show that `"A"^-1 = 1/6("A" - 5"I")`.

Short Answers II | Q 8

Find the adjoint of matrix A = `[(2, 0, -1),(3, 1, 2),(-1, 1, 2)]`

Short Answers II | Q 9

Find the matrix X such that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`

Short Answers II | Q 10

Find the inverse of A = `[(sec theta, tan theta, 0),(tan theta, sec theta, 0),(0, 0, 1)]`

Short Answers II | Q 11

Transform `[(1, 2, 4),(3, -1, 5),(2, 4, 6)]` into an upper triangular matrix by using suitable row transformations

Short Answers II | Q 12

If A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)]` and B = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find the matrix X such that XA = B

Long Answers III

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics Long Answers III

4 Marks

Long Answers III | Q 1

Find the inverse of A = `[(2, -3, 3),(2, 2, 3),(3, -2, 2)]` by using elementary row transformations

Long Answers III | Q 2

If A = `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]`, find A−1 by the adjoint method

Long Answers III | Q 3

Solve the following equations by using inversion method.

x + y + z = −1, x − y + z = 2 and x + y − z = 3

Long Answers III | Q 5

Find the inverse of  A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)]` by elementary column transformations.

Long Answers III | Q 6

If A = `[("x",0,0),(0,"y",0),(0,0,"z")]` is a non-singular matrix, then find A−1 by using elementary row transformations. Hence, find the inverse of `[(2,0,0),(0,1,0),(0,0,-1)]`

Long Answers III | Q 7

Find the inverse of A = `[(costheta, -sintheta, 0),(sintheta, costheta, 0),(0, 0, 1)]` by using elementary row transformations

Long Answers III | Q 8

If A = `[(1,1),(1,2)], "B" = [(4,1),(3,1)]` and C = `[(24,7),(31,9)]`, then find the matrix X such that AXB = C

Long Answers III | Q 9

If A = `[(1, -1, 2),(3, 0, -2),(1, 0, 3)]`, verify that A(adj A) = (adj A)A

Long Answers III | Q 10

If A = `[(2, 3),(1, 2)]`, B = `[(1, 0),(3, 1)]`, find AB and (AB)−1 

Long Answers III | Q 11

Solve the following system of equations by using inversion method

x + y = 1, y + z = `5/3`, z + x = `4/3`

Long Answers III | Q 12

The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is ₹ 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers is ₹ 90. Whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is ₹ 70. Find the cost of each item per dozen by using matrices

Chapter 1: Matrics

MCQVery Short AnswerShort Answers IShort Answers IILong Answers III
12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 1 - Matrics

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 1 (Matrics) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 1 Matrics are Elementry Transformations, Inverse of Matrix, Application of Matrices, Applications of Determinants and Matrices.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Matrics exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in SCERT Maharashtra Question Bank Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exam.

Get the free view of chapter 1 Matrics 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 and can use Shaalaa.com to keep it handy for your exam preparation

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