Use elementary column operation C2 → C2 + 2C1 in the following matrix equation: 2 & 1 2 & 0 = 3 & 1 2 & 0 1 & 0 -1 & 1

2 & 1 2 & 0 = 3 & 1 2 & 0 1 & 0 -1 & 1 Applying C2 → C2 + 2C1 2 & 5 2 & 4 = 3 & 1 2 & 0 1 & 2 -1 & -1

Use elementary column operation C2 → C2 + 2C1 in the following ma…

Write the total number of one-one functions from set A = {1, 2, 3, 4} to set B = {a, b, c}.

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Evaluate the definite integral in Exercise:
$\int_{2}^{3}\frac{1}{\text{x}}\text{dx}$

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If $\theta$ is the angle between the two units vectors $\vec{a}$ and $\vec{b}$ then prove that $\sin \frac{\theta}{2}=\frac{1}{2}|\vec{a}-\vec{b}|$.

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Find the derivative of f given by f(x) = sin^–1 x assuming it exists.

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By using the properties of definite integral, evaluate the integral in Exercise:
$\int\limits_{0}^{\frac{\pi}{2}}\cos^{2}\text{x}\ \text{dx}$

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Let * be a binary operation on the set Q of rational numbers as follows:
a * b = a – b

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Construct a 2 × 3 matrix A = [a_ij] whose elements a_ij are give by:

$\text{a}_\text{ij}=\frac{(\text{i}+\text{j})^2}{2}$

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Find the components along the coordinate axis of the position vector of the following point:

R(-11, -9)

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For the function y = x², if x = 10 and $\triangle\text{x}=0.1$. Find $\triangle\text{y}.$

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Evaluate $\int\frac{(1+\log\text{x})^2}{\text{x}}\text{ dx}$

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