NCERT Solutions, Matrices, Part - 2, Class 12, Maths Notes - Class 12

Class 12: NCERT Solutions, Matrices, Part - 2, Class 12, Maths Notes - Class 12

The document NCERT Solutions, Matrices, Part - 2, Class 12, Maths Notes - Class 12 is a part of Class 12 category.
All you need of Class 12 at this link: Class 12

Matrices and Determinants


Exercise 3.2
Question 1:

Let matrices, mathematics, Question and Answer (Q & A)
Find each of the following

matrices, mathematics, Question and Answer (Q & A)


Answer
matrices, mathematics, Question and Answer (Q & A)
(iv) Matrix A has 2 columns. This number is equal to the number of rows in matrix B.
Therefore, AB is defined as:
matrices, mathematics, Question and Answer (Q & A)


Question 2: Compute the following:
matrices, mathematics, Question and Answer (Q & A)
 

Answer
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

 
Question 3: Compute the indicated products
matrices, mathematics, Question and Answer (Q & A)


Answer
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

 


Question 4:
matrices, mathematics, Question and Answer (Q & A)
Answer

matrices, mathematics, Question and Answer (Q & A)
matrices, mathematics, Question and Answer (Q & A)
 


Question 5:
matrices, mathematics, Question and Answer (Q & A)

Answer

matrices, mathematics, Question and Answer (Q & A)


Question 6: Simplify

matrices, mathematics, Question and Answer (Q & A)


Answer

matrices, mathematics, Question and Answer (Q & A)

 

Question 7: Find X and Y, if
matrices, mathematics, Question and Answer (Q & A)

Answer
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)
From (5) and (6), we have:
matrices, mathematics, Question and Answer (Q & A)
matrices, mathematics, Question and Answer (Q & A)


Question 8:

matrices, mathematics, Question and Answer (Q & A)
 

Answer

matrices, mathematics, Question and Answer (Q & A)


Question 9:
Find x and y, if
matrices, mathematics, Question and Answer (Q & A)


Answer

matrices, mathematics, Question and Answer (Q & A)
Comparing the corresponding elements of these two matrices, we have:

matrices, mathematics, Question and Answer (Q & A)


Question 10: Solve the equation for x, y, z and t if

matrices, mathematics, Question and Answer (Q & A)


Answer

matrices, mathematics, Question and Answer (Q & A)
Comparing the corresponding elements of these two matrices, we get:

matrices, mathematics, Question and Answer (Q & A)


Question 11:
If matrices, mathematics, Question and Answer (Q & A) , find values of x and y.


Answer

matrices, mathematics, Question and Answer (Q & A)
Comparing the corresponding elements of these two matrices, we get:
2x − y = 10 and 3x + y = 5
Adding these two equations, we have:
5x = 15
⇒ x = 3
Now, 3x + y = 5
⇒ y = 5 − 3x
⇒ y = 5 − 9 = −4
∴x = 3 and y = −4


Question 12:
Given
matrices, mathematics, Question and Answer (Q & A) , find the values of x, y, z and w.


Answer

matrices, mathematics, Question and Answer (Q & A)
Comparing the corresponding elements of these two matrices, we get:
matrices, mathematics, Question and Answer (Q & A)


Question 13:
If

matrices, mathematics, Question and Answer (Q & A)


Answer
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


Question 14:
Show that

matrices, mathematics, Question and Answer (Q & A)

 

Answer
matrices, mathematics, Question and Answer (Q & A)
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

 

Question 15:
matrices, mathematics, Question and Answer (Q & A)


Answer
We have A2 = A × A
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


Question 16:
matrices, mathematics, Question and Answer (Q & A)

 

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A) matrices, mathematics, Question and Answer (Q & A)

 

Question 17:
matrices, mathematics, Question and Answer (Q & A)


Answer
matrices, mathematics, Question and Answer (Q & A)

Thus, the value of k is 1.

 


Question 18:
matrices, mathematics, Question and Answer (Q & A)
Answer
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)
Question 19:
A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first
bond pays 5% interest per year, and the second bond pays 7% interest per year. Using
matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds.
If the trust fund must obtain an annual total interest of:
(a) Rs 1,800

(b) Rs 2,000


Answer
(a) Let Rs x be invested in the first bond. Then, the sum of money invested in the second
bond will be Rs (30000 − x).
It is given that the first bond pays 5% interest per year and the second bond pays 7%
interest per year.
Therefore, in order to obtain an annual total interest of Rs 1800, we have:
matrices, mathematics, Question and Answer (Q & A)
Thus, in order to obtain an annual total interest of Rs 1800, the trust fund should invest
Rs 15000 in the first bond and the remaining Rs 15000 in the second bond. (b) Let Rs
x be invested in the first bond. Then, the sum of money invested in the second bond
will be Rs (30000 − x).
Therefore, in order to obtain an annual total interest of Rs 2000, we have:

matrices, mathematics, Question and Answer (Q & A)
Thus, in order to obtain an annual total interest of Rs 2000, the trust fund should invest
Rs 5000 in the first bond and the remaining Rs 25000 in the second bond.

 

Question 20:
The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books,
10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each
respectively. Find the total amount the bookshop will receive from selling all the books
using matrix algebra.


Answer
The bookshop has 10 dozen chemistry books, 8 dozen physics books, and 10 dozen
economics books.
The selling prices of a chemistry book, a physics book, and an economics book are
respectively given as Rs 80, Rs 60, and Rs 40.
The total amount of money that will be received from the sale of all these books can be
represented in the form of a matrix as:

matrices, mathematics, Question and Answer (Q & A)
Thus, the bookshop will receive Rs 20160 from the sale of all these books.


Question 21:
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

 
matrices, mathematics, Question and Answer (Q & A)

NCERT Solutions, Matrices, Part - 2, Class 12, Maths Notes - Class 12

The document NCERT Solutions, Matrices, Part - 2, Class 12, Maths Notes - Class 12 is a part of Class 12 category.
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