Let A= 1&2 -1&3 , B= 4&0 1&5 , C= 2&0 1&-2 , a = 4, b = -2, then show that (A^ T )^ T =A.

We have, A= 1&2 -1&3 , B= 4&0 1&5 , C= 2&0 1&-2 , and a = 4, b = -2 A^ T = 1&2 -1&3 ^ T = 1&-1 2&3 Now, (A^ T )^ T = 1&2 -1&3 ^ T =A Hence proved.

Let A= 1&2 -1&3 , B= 4&0 1&5 , C= 2&0 1&-2 , a = 4, b = -2, then …

State whether $\text{f}(\text{x})=\tan\text{x}-\text{x}$ is increasing or decreasing its domain.

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Two cards are drawn without replacement from a pack of 52 cards. Find the probability that.
Both are kings.

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Evaluate the following integrals:
$\int\tan^3\text{x}\sec^2\text{x}\text{dx}$

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Find the second order derivatives of the function given in Exercise:
$\text{x }\cos\text{x}$

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How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?

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If $\text{f(x)}=\begin{cases}\frac{1-\cos\text{x}}{\text{x}^2},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ is continuous at x = 0, find k.

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Using the property of determinants and without expanding, prove that:
$\begin{vmatrix}0&a&-b\\-a&0&-c\\b&c&0\end{vmatrix}=0$

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If sinx is an integrating factor of the differential equation $\frac{\text{dy}}{\text{dx}}+\text{Py}=\text{Q}$ than write the value of P.

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

$\frac{(\text{i}+\text{j})^2}{2}$

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If A is a square matrix of order 3 with determinant 4, then write the value of |-A|.

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