Find the values of each of the following determinants-1 43272 5-2-313 3-114

(1) nbsp; nbsp;4327=4 #215;7 3 #215;2=28 6=22 (2) nbsp;5 2 31=5 #215;1–2 #215; 3=5 6= 1 (3) nbsp;3 114=3 #215;4–1 #215;1=12+1=13 ...

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Standard IV

Mathematics

Multiplication Trick for a Table

Find the valu...

Question

Find the values of each of the following determinants.

(1) $|\begin{matrix} 4 & 3 \\ 2 & 7 \end{matrix}|$ (2) $|\begin{matrix} 5 & - 2 \\ - 3 & 1 \end{matrix}|$ (3) $|\begin{matrix} 3 & - 1 \\ 1 & 4 \end{matrix}|$

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Solution

(1) $|\begin{matrix} 4 & 3 \\ 2 & 7 \end{matrix}| = 4 \times 7 - 3 \times 2 = 28 - 6 = 22$

(2) $|\begin{matrix} 5 & - 2 \\ - 3 & 1 \end{matrix}| = 5 \times 1 - (- 2) \times (- 3) = 5 - 6 = - 1$

(3) $|\begin{matrix} 3 & - 1 \\ 1 & 4 \end{matrix}| = 3 \times 4 - (- 1) \times 1 = 12 + 1 = 13$

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∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{7}{3} & \frac{5}{3} \frac{3}{2} & \frac{1}{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

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Q. Find the values of following determinants.

(1)

|\begin{matrix} - 1 & 7 \\ 2 & 4 \end{matrix}|

(2)

|\begin{matrix} 5 & 3 \\ - 7 & 0 \end{matrix}|

(3)

|\begin{matrix} \frac{7}{3} & \frac{5}{3} \\ \frac{3}{2} & \frac{1}{2} \end{matrix}|

Subtract.
(i) $3 \frac{1}{3} - 1 \frac{1}{4}$
(ii) $5 \frac{1}{2} - 3 \frac{1}{3}$
(iii) $7 \frac{1}{8} - 6 \frac{1}{10}$
(iv) $7 \frac{1}{2} - 3 \frac{1}{5}$

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∣ ∣ ∣ \begin{matrix} 3 \sqrt{6} & - 4 \sqrt{2} 5 \sqrt{3} & 2 \end{matrix} ∣ ∣ ∣

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Find the values of each of the following determinants. (1) 4327 (2) 5-2-31 (3) 3-114

(1) 4327=4×7-3×2=28-6=22 (2) 5-2-31=5×1--2×-3=5-6=-1 (3) 3-114=3×4--1×1=12+1=13

Find the values of each of the following determinants.

(1) $|\begin{matrix} 4 & 3 \\ 2 & 7 \end{matrix}|$ (2) $|\begin{matrix} 5 & - 2 \\ - 3 & 1 \end{matrix}|$ (3) $|\begin{matrix} 3 & - 1 \\ 1 & 4 \end{matrix}|$

(1) $|\begin{matrix} 4 & 3 \\ 2 & 7 \end{matrix}| = 4 \times 7 - 3 \times 2 = 28 - 6 = 22$

(2) $|\begin{matrix} 5 & - 2 \\ - 3 & 1 \end{matrix}| = 5 \times 1 - (- 2) \times (- 3) = 5 - 6 = - 1$

(3) $|\begin{matrix} 3 & - 1 \\ 1 & 4 \end{matrix}| = 3 \times 4 - (- 1) \times 1 = 12 + 1 = 13$