NCERT 12 Maths Matrices Chapter 3 – Exercise 3.2

ncert 12 maths chapter 3 ex 3.2 ques 1
ncert 12 maths chapter 3 ex 3.2 ans 1
ncert 12 maths chapter 3 ex 3.2 ans 1.1

Note: If two matrices have different orders then we can neither add nor subtract the matrices but we can multiply the matrices either the orders are same or number of columns of first matrix is equal to the number of rows of second matrix.

ncert 12 maths chapter 3 ex 3.2 ques 2
ncert 12 maths chapter 3 ex 3.2 ans 2
ncert 12 maths chapter 3 ex 3.2 ans 2.1
ncert 12 maths chapter 3 ex 3.2 ques 3
ncert 12 maths chapter 3 ex 3.2 ans 3
ncert 12 maths chapter 3 ex 3.2 ans 3.1
ncert 12 maths chapter 3 ex 3.2 ques 4
ncert 12 maths chapter 3 ex 3.2 ans 4
ncert 12 maths chapter 3 ex 3.2 ans 4.1
ncert 12 maths chapter 3 ex 3.2 ques 5
ncert 12 maths chapter 3 ex 3.2 ans 5
ncert 12 maths chapter 3 ex 3.2 ques 6
ncert 12 maths chapter 3 ex 3.2 ques 7
ncert 12 maths chapter 3 ex 3.2 ans 7
ncert 12 maths chapter 3 ex 3.2 ans 7.1
ncert 12 maths chapter 3 ex 3.2 ans 7.2
ncert 12 maths chapter 3 ex 3.2 ques 8
ncert 12 maths chapter 3 ex 3.2 ques 9

By definition of equality of matrix as the given matrices are equal, then corresponding elements are equal. Comparing the corresponding elements, we get
2+y = 5
and 2x+2 = 8
→ y = 5-2 = 3 and 2x=8 – 2 → y=3 and x = 6/2 = 3

ncert 12 maths chapter 3 ex 3.2 ques 10
ncert 12 maths chapter 3 ex 3.2 ques 10.1
ncert 12 maths chapter 3 ex 3.2 ques 11

By definition of equality of matrix as the given matrices are equal, then corresponding elements are equal. Comparing the corresponding elements, we get
2x-y = 10 …… (i)
and 3x+y = 5 ….(ii)
Adding Eq. (i) and (ii), we get
5x = 15 → x = 3
Substituting x = 3 in Eq. (i), we get
2×3 – y=10 → y=6-10 = -4

ncert 12 maths chapter 3 ex 3.2 ques 12

By definition of equality of matrix as the given matrices are equal, then corresponding elements are equal. Comparing the corresponding elements, we get
3x = x+4 → 2x = 4 → x = 2
ncert 12 maths chapter 3 ex 3.2 ques 12.1
Hence, the values of x, y, z and w are 2, 4, 1 and 3

ncert 12 maths chapter 3 ex 3.2 ques 14
ncert 12 maths chapter 3 ex 3.2 ques 14.1
ncert 12 maths chapter 3 ex 3.2 ques 15
ncert 12 maths chapter 3 ex 3.2 ans 15
ncert 12 maths chapter 3 ex 3.2 ans 15.1
ncert 12 maths chapter 3 ex 3.2 ques 16
ncert 12 maths chapter 3 ex 3.2 ans 16
ncert 12 maths chapter 3 ex 3.2 ques 17
ncert 12 maths chapter 3 ex 3.2 ans 17
ncert 12 maths chapter 3 ex 3.2 ans 17.1
ncert 12 maths chapter 3 ex 3.2 ques 18

By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
3k-2 = 1 → k=1
-2k = -2 → k=1
4k = 4 → k=1
-4 = -2k-2 → k=1
Hence k=1

ncert 12 maths chapter 3 ex 3.2 ques 19
ncert 12 maths chapter 3 ex 3.2 ques 19.1
ncert 12 maths chapter 3 ex 3.2 ques 19.2

20.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
Rs. 1800
Rs. 2000
Sol. Let the amount invested in first type of bonds is Rs. x, then that invested in second type of bonds will be Rs. (30,000-x).
According to given condition,
ncert 12 maths chapter 3 ex 3.2 ques 20
Hence, the amounts invested in the two types of bonds are respectively Rs. 15000 and Rs. (30000-15000) = Rs. 15000
ncert 12 maths chapter 3 ex 3.2 ques 20.1
Hence, the amounts invested in two types of bonds are respectively Rs. 5000 and Rs. (30000-5000) = Rs. 25000
21.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.

ncert 12 maths chapter 3 ex 3.2 ques 21

Amount received by the bookseller on selling the types of books can be computed by evaluating the product AB.
ncert 12 maths chapter 3 ex 3.2 ques 21.1

Direction (Q. No. 22 and 23) Assume X, Y, Z, W and P are matrices of orders 2 x n, 3 x k, 2 x p, n x 3 and p x k respectively. Choose the correct answer in Q. 22 and Q. 23
22.The restrictions on n, k and p so that PY + WY will be defined are
k=3, p=n
k is arbitrary, p=2
p is arbitrary
k=2, p=3
Sol. Matrices P and Y are of the orders p x k and 3 x k respectively. Therefore, matrix PY will be defined if k=3. Consequently, PY will be of the order p x k. Matrices W and Y are of the orders n x 3 and 3 x k respectively.
Since the number of columns in W is equal to the number of rows in Y, matrix WY is well defined and of the order n x k
Matrices PY and WY can be added only when their orders are the same. However, PY is of the order p x k and WY is of the order n x k, therefore we must have p = n. Thus, k = 3 and p = n are the restrictions on n, k and p so that PY +WY will be defined. So, correct option is (a).
23.If n = p, then the order of the matrix 7X – 5Z is
P x 2
2 x n
n x 3
p x n
Sol. Matrix X is of the order 2 x n
Therefore, matrix 7X is also of the same order.
Matrix Z is of the order 2 x p i.e., 2 x n [since, n = p]
Therefore, matrix 5Z is also of the same order.
Now both the matrices 7X and 5Z are of the same order 2 x n.
Thus, matrix 7X-5Z is well defined and is of the order 2 x n.
So, correct option is (b)
Updated: October 17, 2020 — 8:45 pm

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