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CUET UG 2025 — Mathematics Statistics & Applications

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Year (x)	2011	2012	2013	2014	2015	2016	2017
Sales (in lakh Rs.) (y)	65	68	70	72	75	67	73

If $y = 70 + 0.964(x - 2014)$ be a straight line trend fitted by the method of the least squares to the above data, then the trend value for the year 2015 is:

Official previous-year question

Held on 15 May 2025 · Verified 13 Jul 2026.

Options

A
70.96
B
72.12
C
76.12
D
75.54

Did you get this right?

Solution

A and B are square symmetric matrices of the same order.

For a symmetric matrix, $A^T = A$ (the matrix equals its own transpose).

Since A and B are symmetric:

$A^T = A$

$B^T = B$

Let $P = AB - BA$

Taking the transpose:

$P^T = (AB - BA)^T$

$P^T = (AB)^T - (BA)^T$

Using the transpose property $(XY)^T = Y^T X^T$ :

$P^T = B^T A^T - A^T B^T$

Substituting $A^T = A$ and $B^T = B$ :

$P^T = BA - AB$

$P^T = -(AB - BA)$

$P^T = -P$

A matrix M is skew-symmetric when $M^T = -M$ .

Since $P^T = -P$ , the matrix $(AB - BA)$ is a skew-symmetric matrix.

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