Download App

Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices1 Mark
Question
Classify the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew- symmetric matrix :

$\left[\begin{array}{ccc}10 & -15 & 27 \\ -15 & 0 & \sqrt{34} \\ 27 & \sqrt{34} & \frac{5}{3}\end{array}\right]$

✓

Answer

Let $A=\left[\begin{array}{ccc}10 & -15 & 27 \\ -15 & 0 & \sqrt{34} \\ 27 & \sqrt{34} & \frac{5}{3}\end{array}\right]$

$\therefore \quad A^T=\left[\begin{array}{ccc}10 & -15 & 27 \\ -15 & 0 & \sqrt{34} \\ 27 & \sqrt{34} & \frac{5}{3}\end{array}\right]$

$\therefore A^{\top}=A, i / e_1, A=A^{\top}$

∴ A is a symmetric matrix.

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 "Answer the following questions in short." from Determinants and Matrices→Determinants and Matrices — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $A=\left[\begin{array}{lrr}2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3\end{array}\right]$, show that $A^2=A$
→
Classify the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew- symmetric matrix :

$\left[\begin{array}{ccc}3 & -2 & 4 \\ 0 & 0 & -5 \\ 0 & 0 & 0\end{array}\right]$

→
$A(1,2), B(2,3)$ and $C(-2,5)$ are vertices of $\triangle \mathrm{ABC}$. Find the slope of the altitude drawn from $\mathrm{A}$.
→
Find the equation of the line : passing through the point $\mathrm{N}(-2,3)$ and the segment of the line intercepted between the co-ordinate axes is bisected at $\mathrm{N}$.
→
Find value of $x$ if
$\begin{aligned} &\left|\begin{array}{lll}x & 3 & 2 \\ x & x & 1 \\ 1 & 0 & 1\end{array}\right|=9\end{aligned}$
→
Classify the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew- symmetric matrix :

$\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & \frac{1}{3}\end{array}\right]$

→
A line passes through points A(xi, y0 and B(h, k). If the slope of the line is m, then show that k – y1 = m (h – x1).
→
$
\begin{aligned}
\text { Let } A & =\left[\begin{array}{ccc}
3 & 2 & -1 \\
-2 & 5 & 4
\end{array}\right]_{2 \times 3}, \\
B & =\left[\begin{array}{cc}
3 & -3 \\
-4 & 2
\end{array}\right]_{2 \times 2}
\end{aligned}
$
Find $\mathrm{AB}$ and $\mathrm{BA}$ which ever exist.
→
$A=\left[\begin{array}{cc}
-1 & -2 \\
-3 & 2 \\
1 & 0
\end{array}\right]_{3 \times 2}, B=\left[\begin{array}{cc}
1 & 2 \\
-1 & -2
\end{array}\right]_{2 \times 2}
$
Find $\mathrm{AB}$ and $\mathrm{BA}$ which ever exist.
→
Following data gives weights of 10 students (in kgs) in a certain school. Find the range of the data 70, 62, 38, 55, 43, 73, 36, 58, 65, 47
→