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XII
Exercise 3
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This number is equal to the number of rows in matrix B
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This number is equal to the number of rows in matrix A
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Also, verify that
Answer
15
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XII
Question 5:
If
then compute
and
Answer
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Answer
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
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XII
⇒x=3
Now, 3x + y = 5
⇒ y = 5 − 3x
⇒ y = 5 − 9 = −4
∴x = 3 and y = −4
Question 12:
Given
, find the values of x, y, z and w
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Answer
25
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XII
Question 14:
Show that
(i)
(ii)
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XII
Answer
(i)
(ii)
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XII
Question 15:
if
Find
Answer
We have A2 = A × A
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XII
29
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XII
Question 16:
If
, prove that
Answer
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XII
Question 17:
If
and
, find k so that
Answer
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XII
Comparing the corresponding elements, we have:
Thus, the value of k is 1
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The first
bond pays 5% interest per year, and the second bond pays 7% interest per year
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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
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It is given that the first bond pays 5% interest per year and the second bond pays 7%
interest per year
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(b) Let Rs
x be invested in the first bond
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Therefore, in order to obtain an annual total interest of Rs 2000, we have:
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
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Their selling prices are Rs 80, Rs 60 and Rs 40 each
respectively
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Answer
The bookshop has 10 dozen chemistry books, 8 dozen physics books, and 10 dozen
economics books
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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:
Thus, the bookshop will receive Rs 20160 from the sale of all these books
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The restriction on n, k and p so that
, and
will be defined are:
A
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k is arbitrary, p = 2
C
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k = 2, p = 3
Answer
Matrices P and Y are of the orders p × k and 3 × k respectively
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Consequently, PY will be of the order p × k
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Since the number of columns in W is equal to the number of rows in Y, matrix WY is
well-defined and is of the order n × k
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However, PY is of the order p × k and WY is of the order n × k
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Thus, k = 3 and p = n are the restrictions on n, k, and p so that
will be defined
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If n = p, then the order of the matrix
Ap×2
B2×n
Cn×3
, and
is
Dp×n
Answer
The correct answer is B
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Therefore, matrix 7X is also of the same order
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e
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Now, both the matrices 7X and 5Z are of the order 2 × n
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