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Componendo and Dividendo

10. If (5a-3b...

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10. If (5a-3b) ÷ a=(4a+b-2c)÷(a+4b-2c)=(a+2b-3c)÷(4a-4c),then prove that, 6a=4b=3c

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Q. Tick (✓) the correct answer:
The sum of (6a + 4b − c + 3), (2b − 3c + 4), (11b − 7a + 2c − 1) and (2c − 5a − 6) is
(a) (4a − 6b + 2)
(b) (−3a + 14b − 3c + 2)
(d) (−6a + 17b)
(d) (−6a + 6b + c −4)

Q. Subtract the sum of

a + 2 b - 3 c

2 c - 3 b - 4 a

from the sum of

5 b - 4 c + a

2 c - 3 b - 4 a

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + b + c 2 a & 3 a + 2 b & 4 a + 3 b + 2 c 3 a & 6 a + 3 b & 10 a + 6 b + 3 c \end{matrix} ∣ ∣ ∣ ∣ = a^{3}

Q. Subtract: [2 MARKS]

(i)

3 a - 4 b + 5 c

4 a - b + 6 c

5 a - 3 b + 2 c

a - 4 b - 2 c

Q. Using properties of determinants, prove that

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + b + c 2 a & 3 a + 2 b & 4 a + 3 b + 2 c 3 a & 6 a + 3 b & 10 a + 6 b + 3 c \end{matrix} ∣ ∣ ∣ ∣ = a^{3}

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