If A= 3 5 2 and B= 1&0&4 , verify that (AB)^T = B^TA^T. - Vidyadip

Question

If $\text{A}=\begin{bmatrix} 3\\5\\2\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0&4\end{bmatrix},$ verify that $(AB)^T = B^TA^T$.

✓

Answer

Given,
$\text{A}=\begin{bmatrix}3\\5\\2 \end{bmatrix},\text{B}=\begin{bmatrix}1&0&4\end{bmatrix}$
$\text{AB}^\text{T}=\text{B}^\text{T}\text{A}^\text{T }$
$\Rightarrow\begin{pmatrix}\begin{bmatrix}3\\5\\2\end{bmatrix}\begin{bmatrix}1&0&4 \end{bmatrix}\end{pmatrix}^\text{T}=\begin{bmatrix}1&0&4\end{bmatrix}^\text{T}\begin{bmatrix}3\\5\\2\end{bmatrix}^\text{T}$
$\Rightarrow\begin{bmatrix}3&0&12\\5&0&20\\2&0&8\end{bmatrix}^\text{T}=\begin{bmatrix}1\\0\\4\end{bmatrix}\begin{bmatrix}3&5&2 \end{bmatrix}$
$\Rightarrow\begin{bmatrix} 3&5&2\\0&0&0\\12&20&8\end{bmatrix}=\begin{bmatrix} 3&5&2\\0&0&0\\12&20&8\end{bmatrix}$
$\Rightarrow\text{LHS}=\text{RHS}$
So,
$(\text{AB})^\text{T}=\text{B}^\text{T}\text{A}^\text{T}$

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 Algebra of Matrices→Algebra of Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals as limit of sum:
$\int\limits^4_{1}\big(\text{x}^2-\text{x}\big)\text{dx}$

Find the points on the curve $y = x^3 - 3x$, where the tangent to the curve is parallel to the chord joining $(1, -2)$ and $(2, 2)$.

Find the angle between the line joining the points (3, -4, -2) and (12, 2, 0) and the plane 3x - y + z = 1.

If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
$\text{If x}=\sqrt{\text{a}^{\sin^{-1}}\text{t}},\text{y}=\sqrt{\text{a}^{\cos^{-1}}\text{t}},\text{ Show that}\frac{\text{dy}}{\text{dx}}=-\frac{\text{y}}{\text{x}}$

Find the shortest distance between the following pairs of lines whose vector equation are:
$\vec{\text{r}}=(8+3\lambda)\hat{\text{i}}-(9+16\lambda)\hat{\text{j}}+(10+7\lambda)\hat{\text{k}}$ and $\vec{\text{r}}=15\hat{\text{i}}+29\hat{\text{j}}+5\hat{\text{k}}+\mu\big(3\hat{\text{i}}+8\hat{\text{j}}-5\hat{\text{k}}\big)$

Maximize $Z = -x_1 + 2x_2$
Subject to
$-\text{x}_1+3\text{x}_2\leq10$
$\text{x}_1+\text{x}_2\leq6$
$\text{x}_1+\text{x}_2\leq2$
$\text{x}_1,\text{x}_2\geq0$

Differentiate the following functions with respect to x:
$(\log\text{x})^{\cos\text{x}}$

Three bags contain a number of red and white balls as follows: Bag $1 : 3$ red balls, Bag $2 : 2$ red balls and $1$ white ball Bag $3 : 3$ white balls.
The probability that bag i will be chosen and a ball is selected from it is $\frac{\text{i}}{6}, i = 1, 2, 3$. What is the probability that:

A red ball will be selected?
A white ball is selected?

If $\text{y}=\tan^{-1}\Big(\frac{\sqrt{1+\text{x}}-\sqrt{1-\text{x}}}{\sqrt{1+\text{x}}+\sqrt{1+\text{x}}}\Big),$ find $\frac{\text{dy}}{\text{dx}}.$

Find the maximum and the minimum values, if any, without using derivaives of the following functions:f(x) = sin2x + 5 on R.