If Δ =
| 2 3+i -1 |
| 3−i 0 i−1 |
| -1 -1−i -1 |
then what is A + B equal to?
-6
We first compute the matrix operations and then simplify to find that A + B = -6.
How many matrices of different orders are possible with elements comprising all prime numbers less than 30?
If (a - b) (b - c) (c - a) = 2 and abc = 6, then what is the value of \(\begin{vmatrix}a & b & c \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3 \end{vmatrix}?\)
Under which of the following conditions does the determinant \(\begin{vmatrix}a & b & c \\ b & c & a \\ c & a & b\end{vmatrix}\) vanish?
1. a + b + c = 0
2. a 3+ b 3+ c 3= 3abc
3. a 2+ b 2+ c 2- ab - bc - ca = 0
Select the correct answer using the code given below:
If \(ABC\) is a triangle, then what is the value of the determinant
\(\begin{vmatrix}\cos C & \sin B & 0 \\\tan A & 0 & \sin B \\0 & \tan(B+C) & \cos C\end{vmatrix}?\)
If \(a, b, c\) are the sides of triangle \(ABC\), then what is
\(\begin{vmatrix}a^2 & b\sin A & c\sin A \\b\sin A & 1 & \cos A \\c\sin A & \cos A & 1\end{vmatrix} equal to ?\)
If in a triangle ABC, sin3A + sin3B + sin3C = 3sinAsinBsinc, then what is the value of the determinant \(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b\end{vmatrix}\) where a,b,c are sides of the triangle?
For what value of $n$ is the determinant
$[\begin{vmatrix}C\binom{9}{4} & C\binom{9}{3} & C\binom{10}{n-2} \\C\binom{11}{6} & C\binom{11}{5} & C\binom{12}{n} \\C\binom{m}{7} & C\binom{m}{6} & C\binom{m+1}{n+1} \end{vmatrix} = 0]$
for every $m > n$?
If B is a non-singular matrix and A is a square matrix, then the value of det (B -1 AB) is equal to
Which of the following determinants have value zero?
1. \(\left| {\begin{array}{*{20}{c}} {41}&1&5\\ {79}&7&9\\ {29}&5&3 \end{array}} \right|\)
2. \(\left| {\begin{array}{*{20}{c}} 1&a&{b + c}\\ 1&b&{c + a}\\ 1&c&{a + b} \end{array}} \right|\)
3. \(\left| {\begin{array}{*{20}{c}} 0&c&b\\ { - c}&0&a\\ { - b}&{ - a}&0 \end{array}} \right|\)
Select the correct answer using the code given below.
If A is an invertible matrix of order n and k is any positive real number, then the value of [det(kA)] -1 det A is
The determinant of the matrix $\begin{pmatrix} 1 & p & q + r \\ 1 & q & r + p \\ 1 & r & p + q \end{pmatrix}$ is ______.
Let $f(x) = \begin{vmatrix} x^3 & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^2 & p^3 \end{vmatrix}$
where $p$ is a constant.
The value of $\frac{d^3}{dx^3}f(x)$ at $x = 0$ is
How many matrices of different orders are possible with elements comprising all prime numbers less than 30?
If A is a square matrix of order 3 and det A = 5, then what is det [(2A) -1 ] equal to ?