Students can Download Basic Maths Exercise 1.1 Questions and Answers, Notes Pdf, 2nd PUC Basic 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 Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1

Part – A

2nd PUC Basic Maths Matrices and Determinants Ex 1.1 One Mark Questions and Answers

Question 1.
If A = \(\left[ \begin{matrix} 1 & -2 \\ 3 & 4 \end{matrix} \right]\) . Find 2A and 3A
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 1

Question 2.
If A = \(\left[ \begin{matrix} 1 & -3 & 5 \\ 6 & 2 & 4 \end{matrix} \right]\) find 5A’.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 2

KSEEB Solutions

Question 3.
If A = \(\left[ \begin{matrix} 1 & 2 & 4 \\ -1 & 3 & -2 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 3 & -4 & -1 \\ 1 & 5 & -2 \end{matrix} \right]\) .Find A+ B and A – B
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 3

Question 4.
If  \(\left[ \begin{matrix} x+y & 3 \\ 2 & -y+x \end{matrix} \right] +\left[ \begin{matrix} 2 & 3 \\ 4 & 1 \end{matrix} \right] =\left[ \begin{matrix} 0 & 6 \\ 6 & 0 \end{matrix} \right]\) . Find x and y.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 5

Question 5.
If  \(\left[ \begin{matrix} { x }^{ 2 } & 1 \\ 2 & -1 \end{matrix} \right] +\left[ \begin{matrix} 2x & 2 \\ -1 & 2 \end{matrix} \right] =\left[ \begin{matrix} -1 & 3 \\ 1 & 1 \end{matrix} \right]\) Find x.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 7
⇒ x2 + 2x = -1
x2 + 2x + 1 = 0
(x + 1)2 = 0 ⇒ x + 1 = 0
⇒ x = -1

KSEEB Solutions

Question 6.
If A = \(\left[ \begin{matrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{matrix} \right]\) . Find A – A’
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 8
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 9

Question 7.
If A = \(\left[ \begin{matrix} 2 & -x \\ x & -7 \end{matrix} \right]\) . Find A + A’.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 10

Question 8.
If A = \(\left[ \begin{matrix} 1 & 2 \\ 3 & -1 \end{matrix} \right]\) B = \(\left[ \begin{matrix} 2 & 5 \\ -3 & -1 \end{matrix} \right]\) C = \(\left[ \begin{matrix} 1 & -1 \\ 4 & -3 \end{matrix} \right]\) Find 2A – 3B – C
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 11

KSEEB Solutions

Question 9.
Find the matrix A. if 2A + B = \(\left[ \begin{matrix} 2 & 0 \\ 1 & -3 \end{matrix} \right]\) , where u = \(\left[ \begin{matrix} 1 & -1 \\ 3 & 0 \end{matrix} \right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 12

Question 10.
If A = \(\left[ \begin{matrix} 3 & -1 \\ 4 & 5 \end{matrix} \right]\) , Find X such that A – 2x = \(\left[ \begin{matrix} 1 & 4 \\ 2 & -3 \end{matrix} \right]\) .
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 13

Question 11.
If A + B + C = 0 where A = \(\left[ \begin{matrix} 3 & -2 \\ 2 & 0 \\ 1 & 4 \end{matrix} \right]\) , B = \(\left[ \begin{matrix} 2 & -1 \\ -4 & 2 \\ -3 & 3 \end{matrix} \right]\) . Find C
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 14

KSEEB Solutions

Question 12.
If A = B = \(\left[ \begin{matrix} 3 & 1 \\ -3 & 4 \end{matrix} \right]\) verify (A – B)’ = A’ – B’
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 15

Part – B

2nd PUC Basic Maths Matrices and Determinants Ex 1.1 Two Marks Questions and Answers

Question 1.
If A = \(\left[ \begin{matrix} 4 & -1 \\ 0 & 3 \\ 2 & -3 \end{matrix} \right]\) . Find (i) \(\frac{5 A}{2} (ii) \frac{-2 A}{3}\) .
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 16

KSEEB Solutions

Question 2.
If A = \(\left[ \begin{matrix} 1 & 3 & -1 \\ -1 & 0 & 2 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 4 & -1 & 2 \\ 1 & 3 & -2 \end{matrix} \right]\) . Find (i) 2A + 3B (ii) A – 3B (iii) A + \(\frac { 1 }{ 2 }\)B.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 17
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 18

Question 3.
If A = \(\left[ \begin{matrix} 3 & 2 \\ 1 & 4 \end{matrix} \right]\) B = \(\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right]\) and C = \(\left[ \begin{matrix} -3 & 4 \\ 2 & -1 \end{matrix} \right]\) . Find 34A – 2B – 4C
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 19

KSEEB Solutions

Question 4.
If A = \(\left[ \begin{matrix} 1 & -3 \\ -4 & -1 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 3 & 4 \\ -5 & 1 \end{matrix} \right]\) and 0 is a null matrix of order 2 × 2. Find the matrix C such that
(i) 2C = A + B
(ii) A + C = 0
(iii) B + 5c = A
(iv) 3A + 5B + 2C = 0
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 20
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 21

Question 5.
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 22
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 23

KSEEB Solutions

Question 6.
Find x and y given that \(\left[ \begin{matrix} -9 \\ 2 \end{matrix} \right] \quad -\quad \left[ \begin{matrix} 5 \\ -1 \end{matrix} \right] =\quad \left[ \begin{matrix} x \\ y \end{matrix} \right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 24

Question 7.
If A = \(\left[ \begin{matrix} 3 & 1 & 4 \\ 5 & 6 & 3x+1 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 6 \\ 4 & 3 \end{matrix} \right]\) .
Find x given that A = B’
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 25

Question 8.
Solve for x and y \(x\left[ \begin{matrix} 2 \\ 1 \end{matrix} \right] +y\left[ \begin{matrix} 3 \\ 5 \end{matrix} \right] +\left[ \begin{matrix} 4 \\ 6 \end{matrix} \right] =\left[ \begin{matrix} 12 \\ 17 \end{matrix} \right]\) .
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 26
⇒ 2x + 3y + 4 = 12
x + 5y + 6 = 7
⇒ 2x + 3y = 8 …. (1) solving these equations
x + 5y = 11 ….. (2) × 2
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 27
and x = 11 – 5y = 11 – 10 = 1
∴ x = 1, y = 2

KSEEB Solutions

Question 9.
Find x and y given that \(\left[ \begin{matrix} x+y & 3 \\ -1 & x-y \end{matrix} \right] =\left[ \begin{matrix} 4 & 3 \\ -1 & 8 \end{matrix} \right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 28

Question 10.
If \(\left[ \begin{matrix} 2 & 3 \\ 7 & 5 \end{matrix} \right] +\left[ \begin{matrix} 2 & x-2 \\ y-1 & 5 \end{matrix} \right] =\left[ \begin{matrix} 4 & 1 \\ 7 & 10 \end{matrix} \right]\) Find x and y-1
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 29
⇒x + 1 = 1 ⇒ x = 0
y + 6 = 7 ⇒ y = 1
∴ x = 0, y = 1

Part – C

2nd PUC Basic Maths Matrices and Determinants Ex 1.1 Three Marks Questions and Answers

Question 1.
Find A and B if
(a) 2A + B = \(\left[ \begin{matrix} 1 & -1 \\ 0 & 1 \end{matrix} \right]\) and A – 3B = \(\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \right]\) .
(b) 2A + B = \(\left[ \begin{matrix} 2 & 3 & 1 \\ 1 & 4 & 0 \end{matrix} \right]\) , 3A + B = \(\left[ \begin{matrix} 4 & 6 & 1 \\ 2 & 3 & 5 \end{matrix} \right]\)
(c) 2A – 3B = \(\left[ \begin{matrix} 2 & -4 \\ -12 & 1 \end{matrix} \right]\) , A + 5B = \(\left[ \begin{matrix} 1 & 24 \\ 33 & 7 \end{matrix} \right]\)
(d) 2A + B = \(\left[ \begin{matrix} 3 & -1 \\ -2 & 5 \end{matrix} \right]\) and A – 2B = \(\left[ \begin{matrix} 4 & 2 \\ -1 & 5 \end{matrix} \right]\) .
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 30
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 31
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 32
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 33

KSEEB Solutions

Question 2.
If A = \(\left[ \begin{matrix} 3 & 8 & 1 \\ 2 & -6 & 3 \\ 7 & 4 & -5 \end{matrix} \right]\) , B = \(\left[ \begin{matrix} 4 & 0 & 2 \\ 6 & 2 & 3 \\ 1 & 3 & 2 \end{matrix} \right]\) . verify 3(A + B) = 3A + 3B.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 34
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 35

Question 3.
Find x, y, a, b if = \(\left[ \begin{matrix} 3x+4y & 2 & x-2y \\ a+b & 2a-b & -1 \end{matrix} \right] =\left[ \begin{matrix} 2 & 2 & 4 \\ 5 & -5 & -1 \end{matrix} \right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 36

Question 4.
Find x if \(\left[ \begin{matrix} { x }^{ 3 } & 1 \\ 3 & 3 \end{matrix} \right] +\left[ \begin{matrix} { -2x }^{ 2 } & 3 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} -x & 4 \\ 4 & 7 \end{matrix} \right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 37
⇒ x3 – 2x2 = x; x3 – 2x2 + x = 0 ; x(x2 – 2x + 1) = 0
x = 0 or (x – 1)2 = 0 ⇒ x = 0 or x = 1

KSEEB Solutions

Question 5.
If A = \(\left[ \begin{matrix} 2 & -1 & 3 \\ -2 & 1 & 0 \end{matrix} \right]\) , B = \(\left[ \begin{matrix} -1 & 0 & 4 \\ 5 & 1 & -3 \end{matrix} \right]\) C = \(\left[ \begin{matrix} 4 & -1 & 1 \\ 6 & 2 & -1 \end{matrix} \right]\) . Find the matrix X such that 2A – 3B – x = C
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 38

Question 6.
Find a,b,c given that \(4\left[ \begin{matrix} a & 2 & 3 \\ 4 & 5 & -6 \\ 7 & -8 & 9 \end{matrix} \right] -5\left[ \begin{matrix} 3 & 2 & 1 \\ b & 6 & -4 \\ 9 & -8 & 7 \end{matrix} \right] =\left[ \begin{matrix} 13 & -2 & 7 \\ 6 & -5 & -4 \\ -17 & 2c & 1 \end{matrix} \right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.1 - 39