Download App

Algebra — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSAlgebra5 Marks
Question
Let $A=\left[\begin{array}{ll}1 & 2 \\ 1 & 3\end{array}\right], B=\left[\begin{array}{ll}4 & 0 \\ 1 & 5\end{array}\right], C=\left[\begin{array}{ll}2 & 0 \\ 1 & 2\end{array}\right]$ Show that $(A-B)^{\top}=A^{\top}-B^{\top}$
✓

Answer

$
\begin{aligned}
& A=\left[\begin{array}{ll}
1 & 2 \\
1 & 3
\end{array}\right], B=\left[\begin{array}{ll}
4 & 0 \\
1 & 5
\end{array}\right], C=\left[\begin{array}{ll}
2 & 0 \\
1 & 2
\end{array}\right] \\
& A-B=\left[\begin{array}{ll}
1 & 2 \\
1 & 3
\end{array}\right]-\left[\begin{array}{ll}
4 & 0 \\
1 & 5
\end{array}\right] \\
& =\left[\begin{array}{ll}
-3 & 2 \\
0 & 2
\end{array}\right] \\
& (A-B)^{\top}=\left[\begin{array}{ll}
-3 & 0 \\
2 & -2
\end{array}\right] \ldots(1) \\
& A^{\top}=\left[\begin{array}{ll}
1 & 1 \\
2 & 3
\end{array}\right] \\
& B^{\top}=\left[\begin{array}{ll}
4 & 1 \\
0 & 5
\end{array}\right] \\
& A^{\top}-B^{\top}=\left[\begin{array}{ll}
1 & 1 \\
2 & 3
\end{array}\right]-\left[\begin{array}{ll}
4 & 1 \\
0 & 5
\end{array}\right] \\
& =\left[\begin{array}{ll}
-3 & 0 \\
2 & -2
\end{array}\right] \ldots(2)
\end{aligned}
$

From (1) and (2) we get
$(A-B)^{\top}=A^{\top}-B^{\top}$

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 Mark Questions]" from Algebra→Algebra — all question types→MATHS STD 10 question papers→Tamilnadu Board STD 10 question papers→Tamilnadu Board question paper generator→

Similar questions

Simplify $\frac{4 x}{x^2-1}-\frac{x+1}{x-1}$
→
A girl looks the reflection of the top of the lamp post on the mirror which is 6.6 m away from the foot of the lamppost. The girl whose height is 1.25 m is standing 2.5 m away from the mirror. Assuming the mirror is placed on the ground facing the sky and the girl, mirror and the lamppost are in the same line, find the height of the lamp post.
→
An aeroplane at an altitude of $1800 m$ finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are $60^{\circ}$ and $30^{\circ}$ respectively. Find the distance between the two boats. $(\sqrt{3}=1.732)$
→
The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle
→
If $A=\left[\begin{array}{lll}5 & 2 & 9 \\ 1 & 2 & 8\end{array}\right], B=\left[\begin{array}{cc}1 & 7 \\ 1 & 2 \\ 5 & -1\end{array}\right]$ verify that $(A B)^{\top}=B^{\top} A^{\top}$
→
The barrel of a fountain-pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used for writing 330 words on an average. How many words can be written using a bottle of ink containing one-fifth of a litre?
→
Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents.
→
Solve the following quadratic equation by factorization method
$
\sqrt{ a ( a -7)}=3 \sqrt{2}
$
→
In a theatre, there are 20 seats in the front row and 30 rows were allotted. Each successive row contains two additional seats than its front row. How many seats are there in the last row?
→
Draw the graph of $y=x^2+3 x+2$ and use it to solve $x^2+2 x+1=0$
→