10th Maths Book Back Question and Answers – Chapter 3 Exercise 3.16:
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Samacheer Kalvi 10th Maths Book Back Answers – Ex 3.16 Algebra
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Chapter 3
Exercise 3.16 Algebra
1. In the matrix A = ⎡⎣⎢⎢⎢⎢8−11697–√4843√23−113501⎤⎦⎥⎥⎥⎥
(i) The number of elements
(ii) The order of the matrix
(iii) Write the elements a22, a23, a24, a34, a43, a44
Solution:
(i) 16
(ii) 4 × 4
(iii) 7–√,3√2, 5, 0, -11, 1
2. If a matrix has 18 elements, what possible orders can it have? What if it has 6 elements?
Solution:
1 × 18, 2 × 9, 3 × 6, 6 × 3, 9 × 2, 18 × 1 and 1 × 6, 2 × 3, 3 × 2, 6 × 1
3. Construct a 3 × 3 matrix whose elements are given by then find the transpose of A.
(i) aij = |i – 2j|
(ii) aij = (i+j)33
Solution:
(i) aij = |i – 2j|
a11 = |1 – 2 × 1| = |1 – 2| = |-1| = 1
a12 = |1 – 2 × 2| = |1 – 4| = |-3| = 3
a13 = |1 – 2 × 3| = |1 – 6| = |-5| = 5
a21 = |2 – 2 × 1| = |2 – 2| = 0
a22 = |2 – 2 × 2| = |2 – 4| = |-2| = 2
a23 = |2 – 2 × 3| = |2 – 6| = |-4| = 4
a31 = |3 – 2 × 1| = |3 – 2| = |1| = 1
a32 = |3 – 2 × 2| = |3 – 4| = |-1| = 1
a33 = |3 – 2 × 3| = |3 – 6| = |-3| = 3
∴ ⎡⎣⎢101321543⎤⎦⎥ is the required 3 × 3 matrix
4.
Solution:
5.
Solution:
6.
Solution:
7.Find the values of x,y and z from the following equations
Solution:
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