# CLASS-10MATRIX - PROBLEM & SOLUTION

MATRIX - PROBLEM & SOLUTION -

Example.1) Construct a 2 X 3 matrix, whose elements aᵢₑ  are given by aᵢₑ = (i + e)

Ans.) The required matrix has 2 rows and 3 columns. It is given by – now, a₁₁ = (1 + 1) = 2,

a₁₂ = (1 + 2) = 3,

a₁₃ = (1 + 3) = 4,

a₂₁ = (2 + 1) = 3,

a₂₂ = (2 + 2) = 4,

a₂₃ = (2 + 3) = 5, Example.2) If a matrix has 8 elements, what are the possible orders it can have ?

Ans.)  Since all matrices of order (1 X 8), (8 X 1), (2 X 4), or (4 X 2) contains 8 elements, a matrix containing 8 elements can have any of the following orders –

(1 X 8), (8 X 1), (2 X 4), or (4 X 2)         (Ans.)

Example.3) If a matrix has 12 elements, what are the possible orders it can have ?

Ans.)  Since all matrices of order (1 X 12), (12 X 1), (3 X 4), (4 X 3), (6 X 2), or (2 X 6) contains 12 elements, a matrix containing 12 elements can have any of the following orders –

(1 X 12), (12 X 1), (3 X 4), (4 X 3), (6 X 2), or (2 X 6)    (Ans.) we know that the corresponding elements of equal matrices are equal.

So, 2 = c, a = 3, b = 1, and -6 = c – 2d

Thus we have, a = 3, b = 1, and  c = 2.

Also, -6 = c – 2d

=>   - 6 = 2 – 2d    (substitute the value of c = 2)

=>   - 2d = - 8

=>      d = 4

So, the value of a, b, c, & d is 3, 1, 2, & 4 respectively.   (Ans.) 2x + 3y = 3 ……………..(i)

3x – 2y = 11 ……………….(ii)

a – 2b = 8 ………………(iii)

2a + b = 6 ………………(iv)

Multiplying (i) by 2 and multiplying (ii) by 3 and we get –

4x + 6y = 6 ……………(v)

9x – 6y = 33 …………..(vi)

Now, adding (v) and (vi), and we get –

4x + 6y = 6

9x - 6y =  33

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13x  = 39

=>          x  =  3

Now putting the value of x = 3 in (v) and we get -

4x + 6y = 6

=>   (4 X 3) + 6y = 6

=>    12 + 6y = 6

=>    2 + y = 1

=>    y = - 2 + 1 = - 1

Multiplying (iii) by 1 and multiplying (iv) by 2 and we get –

a – 2b = 8 ………………(vii)

4a + 2b = 12 ………………(viii)

Now, we will add (vii) & (viii), and we get –

a – 2b = 8

4a + 2b = 12

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5a  =  20

=>       a = 4

Now, we will substitute the value of a = 4 in (iv), and we get -

2a + b = 6

=>      (2 X 4) + b  = 6

=>      8 + b = 6

=>      b = - 8 + 6 = - 2

Hence, a = 4, b = - 2, x = 3, and y = - 1           (Ans.)