If A= -2 4 5 ,B= 1&3&-6 , verify that (AB)^T = B^TA^T - Vidyadip

Question

If $\text{A}=\begin{bmatrix}-2\\4\\5\end{bmatrix},\text{B}=\begin{bmatrix}1&3&-6\end{bmatrix},$ verify that $(AB)^T = B^TA^T$

✓

Answer

Given: $\text{A}=\begin{bmatrix}-2\\4\\5\end{bmatrix}$
$\text{A}^\text{T}=\begin{bmatrix}-2&4&5\end{bmatrix}$
$\text{B}=\begin{bmatrix}1&3&-6\end{bmatrix}$
$\text{B}^\text{T}=\begin{bmatrix}1\\3\\-6\end{bmatrix}$
Now,
$\text{AB}=\begin{bmatrix}-2\\4\\5\end{bmatrix}\begin{bmatrix}1&3&-6\end{bmatrix}$
$\Rightarrow\text{AB}=\begin{bmatrix}-2&-6&12\\4&12&-24\\5&15&-30\end{bmatrix}$
$\Rightarrow(\text{AB})^\text{T}=\begin{bmatrix}-2&4&5\\-6&12&15\\12&-24&-30\end{bmatrix}\ \dots(1)$
$\text{B}^\text{T}\text{A}^\text{A}=\begin{bmatrix}1\\3\\-6\end{bmatrix}\begin{bmatrix}-2&4&5\end{bmatrix}$
$\Rightarrow\text{B}^\text{T}\text{A}^\text{T}=\begin{bmatrix}-2&4&5\\-6&12&15\\12&-24&-30\end{bmatrix}\ \dots(2)$
$\therefore\ (\text{AB})^\text{T}=\text{B}^\text{T}\text{A}^\text{T} [$From eqs. $(1)$ and $(2)]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from MATRICES→MATRICES — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Solve the following differential equation:
$\cos^2(\text{x}-2\text{y}) = 1-2\frac{\text{dy}}{\text{dx}}$

Suppose we have four boxes A,B,C and D containing coloured marbles as given below:

Box	Marble colour
	Red	White	Black
A	1	6	3
B	6	2	2
C	8	1	1
D	0	6	4

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of the following functions. Also, find the points of inflection,
$f(x) = (x - 1)(x - 2)^2$

If the area bounded by the parabola $\text{y}^{2} = 16\text{ax}$ and the line $\text{y = 4 mx}$ is $\frac{\text{a}^{2}}{12}$ sq. units, then using integration, find the value of m.

Find the area of the region bounded by the curve $y = x - 1$ and $(y - 1)^2 = 4(x + 1).$

Find the area bounded by the parabola $y^2 = 4x$ and the line $y = 2x - 4:$
By using horizontal strips.

Given $\text{A}=\begin{bmatrix}2&2&-4\\-4&2&-4\\2&-1&5\end{bmatrix},\text{B}=\begin{bmatrix}1&-1&0\\2&3&4\\0&1&2\end{bmatrix}$ , find $BA$ and use this to solve the system of equations $y + 2z = 7, x - y = 3, 2x + 3y + 4z = 17$

A bank pays interest by continuous compounding, that is, by treating the interest rate as the instantaneous rate of change of principal. Suppose in an account interest accrues at $8\%$ per year, compounded continuously. Calculate the percentage increase in such an account over one year.

Evaluate the following intregals:
$\int\frac{1}{\text{x}\log\text{x}(2+\log\text{x})}\text{ dx}$

The probabilities of two students A and B coming to the school in time are $\frac{3}{7}$ and $\frac{5}{7}$ respectively. Assuming that the events, 'A coming in time' and 'B coming in time' are independent, find the probability of only one of them coming to the school in time. Write at least one advantage of coming to school in time.