If A = [ ccc 1 & 2 & -5 2 & -3 & 4 -5 & 4 & 9 ], prove that A ^ =… - Vidyadip

Question

If $A =\left[\begin{array}{ccc}1 & 2 & -5 \\ 2 & -3 & 4 \\ -5 & 4 & 9\end{array}\right]$, prove that $A ^{\top}= A$.

✓

Answer

$
\begin{gathered}
A=\left[\begin{array}{rrr}
1 & 2 & -5 \\
2 & -3 & 4 \\
-5 & 4 & 9
\end{array}\right]....(1) \\
\therefore A^{ T }=\left(\begin{array}{rrr}
1 & 2 & -5 \\
2 & -3 & 4 \\
-5 & 4 & 9
\end{array}\right)\ldots(2)
\end{gathered}
$
From (1) and (2), $A ^{ T }= A$.

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 "Solve the Following Question.(2 Marks)" from Matrices (p-1)→Matrices (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Evalute : $\int x e^{2 x} d x$

Evalute : $\int \frac{1}{a^2-b^2 x^2} d x$

Find the value Index Number using the Simple Aggregate Method.
Find x if the Price Index Number by Simple Aggregate Method is 125

Commodity	P	Q	R	S	T
Base Year Price (in Rs.)	8	12	16	22	18
Current Year Price (in Rs.)	12	18	x	28	22

If $A=\left[\begin{array}{ccc}1 & 2 & -3 \\ -3 & 7 & -8 \\ 0 & -6 & 1\end{array}\right], B=\left[\begin{array}{ccc}9 & -1 & 2 \\ -4 & 2 & 5 \\ 4 & 0 & -3\end{array}\right]$, then find the matrix $C$ such that $A + B + C$ is a zero matrix.

Express the truth of each of the following statements by Venn diagrams : No circles are polygons.

Evalute : $\int x \sqrt{1+x^2} d x$

Evalute : $\int \sqrt{x^2-8 x+7} d x$

Solve the following differential equations : $d y+(2 y) d x=8 d x$

Form the differential equation by eliminating arbitrary constants from the relation $b x+a y=a b$.

Calculate the cost of living index.

Group	Food	Clothing	Fuel & Lighting	House Rent	Miscellaneous
I	180	120	300	100	160
W	4	5	6	x	3