Write the value of the determinant pp -1 p -1 p -

Pp+1p 1p=p2 p+1p 1 #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #16 ...

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Standard XII

Mathematics

nth Term of A.P

Write the val...

Question

Write the value of the determinant $|\begin{matrix} p & p + 1 \\ p - 1 & p \end{matrix}|$ .

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Solution

$|\begin{matrix} p & p + 1 \\ p - 1 & p \end{matrix}| = p^{2} - (p + 1) (p - 1) = p^{2} - (p^{2} - 1) = p^{2} - p^{2} + 1 = 1$

Hence, the value of the determinant $|\begin{matrix} p & p + 1 \\ p - 1 & p \end{matrix}|$ is 1.

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Similar questions

Q. Write the value of the determinant

[\begin{matrix} p & p + 1 p - 1 & p \end{matrix}]

when

p = 1342

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Question 2

Complete the entries of the third column of the table:

$\begin{matrix} S.No & Equation & Value of Variable & Equation satisfied Yes/No (a) & 10 y = 80 & y = 10 (b) & 10 y = 80 & y = 8 (c) & 10 y = 80 & y = 5 (d) & 4 l = 20 & l = 20 (e) & 4 l = 20 & l = 80 (f) & 4 l = 20 & l = 5 (g) & b + 5 = 9 & b = 5 (h) & b + 5 = 9 & b = 9 (i) & b + 5 = 9 & b = 4 (j) & h - 8 = 5 & h = 13 (k) & h - 8 = 5 & h = 8 (l) & h - 8 = 5 & h = 0 (m) & p + 3 = 1 & p = 3 (n) & p + 3 = 1 & p = 1 (o) & p + 3 = 1 & p = 0 (p) & p + 3 = 1 & p = - 1 (q) & p + 3 = 1 & p = - 2 \end{matrix}$

Q. The sum of first

p

-terms of a sequence is

p (p + 1) (p + 2)

. The

10^{t h}

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Q. The value of

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p^{2} = \frac{1}{p}

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Write the value of the determinant pp+1p-1p.

pp+1p-1p=p2-p+1p-1 =p2-p2-1 =p2-p2+1 =1 Hence, the value of the determinant pp+1p-1p is 1.

Write the value of the determinant $|\begin{matrix} p & p + 1 \\ p - 1 & p \end{matrix}|$ .

$|\begin{matrix} p & p + 1 \\ p - 1 & p \end{matrix}| = p^{2} - (p + 1) (p - 1) = p^{2} - (p^{2} - 1) = p^{2} - p^{2} + 1 = 1$

Hence, the value of the determinant $|\begin{matrix} p & p + 1 \\ p - 1 & p \end{matrix}|$ is 1.