Show that
\[\begin{vmatrix}x + 1 & x + 2 & x + a \\ x + 2 & x + 3 & x + b \\ x + 3 & x + 4 & x + c\end{vmatrix} =\text{ 0 where a, b, c are in A . P .}\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
\[If \begin{vmatrix}p & b & c \\ a & q & c \\ a & b & r\end{vmatrix} = 0,\text{ find the value of }\frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c}, p \neq a, q \neq b, r \neq c .\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Show that x = 2 is a root of the equation
\[\begin{vmatrix}x & - 6 & - 1 \\ 2 & - 3x & x - 3 \\ - 3 & 2x & x + 2\end{vmatrix} = 0\] and solve it completely.
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Solve the following determinant equation:
\[\begin{vmatrix}x + a & b & c \\ a & x + b & c \\ a & b & x + c\end{vmatrix} = 0\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Solve the following determinant equation:
\[\begin{vmatrix}x + a & x & x \\ x & x + a & x \\ x & x & x + a\end{vmatrix} = 0, a \neq 0\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Solve the following determinant equation:
\[\begin{vmatrix}3x - 8 & 3 & 3 \\ 3 & 3x - 8 & 3 \\ 3 & 3 & 3x - 8\end{vmatrix} = 0\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Solve the following determinant equation:
\[\begin{vmatrix}1 & x & x^2 \\ 1 & a & a^2 \\ 1 & b & b^2\end{vmatrix} = 0, a \neq b\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Solve the following determinant equation:
\[\begin{vmatrix}x + 1 & 3 & 5 \\ 2 & x + 2 & 5 \\ 2 & 3 & x + 4\end{vmatrix} = 0\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Solve the following determinant equation:
\[\begin{vmatrix}1 & x & x^3 \\ 1 & b & b^3 \\ 1 & c & c^3\end{vmatrix} = 0, b \neq c\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Solve the following determinant equation:
\[\begin{vmatrix}1 & 1 & x \\ p + 1 & p + 1 & p + x \\ 3 & x + 1 & x + 2\end{vmatrix} = 0\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Solve the following determinant equation:
\[\begin{vmatrix}15 - 2x & 11 - 3x & 7 - x \\ 11 & 17 & 14 \\ 10 & 16 & 13\end{vmatrix} = 0\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Let \[A = \begin{bmatrix}3 & 2 & 7 \\ 1 & 4 & 3 \\ - 2 & 5 & 8\end{bmatrix} .\] Find matrices X and Y such that X + Y = A, where X is a symmetric and Y is a skew-symmetric matrix
[3] Matrices
Chapter: [3] Matrices
Concept: undefined >> undefined
Define a symmetric matrix. Prove that for
\[A = \begin{bmatrix}2 & 4 \\ 5 & 6\end{bmatrix}\],
A +
AT is a symmetric matrix where
AT is the transpose of
A.
[3] Matrices
Chapter: [3] Matrices
Concept: undefined >> undefined
Solve the following determinant equation:
\[\begin{vmatrix}3 & - 2 & \sin\left( 3\theta \right) \\ - 7 & 8 & \cos\left( 2\theta \right) \\ - 11 & 14 & 2\end{vmatrix} = 0\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Express the matrix \[A = \begin{bmatrix}3 & - 4 \\ 1 & - 1\end{bmatrix}\] as the sum of a symmetric and a skew-symmetric matrix.
[3] Matrices
Chapter: [3] Matrices
Concept: undefined >> undefined
Show that
`|(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma)|=0`, where α, β, γ are in A.P.
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
If a, b, c are real numbers such that
\[\begin{vmatrix}b + c & c + a & a + b \\ c + a & a + b & b + c \\ a + b & b + c & c + a\end{vmatrix} = 0\] , then show that either
\[a + b + c = 0 \text{ or, } a = b = c\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
If \[A = \begin{bmatrix}2 & 3 \\ 5 & 7\end{bmatrix}\] , find
A +
AT.
[3] Matrices
Chapter: [3] Matrices
Concept: undefined >> undefined
If \[A = \begin{bmatrix}i & 0 \\ 0 & i\end{bmatrix}\] , write
A2.
[3] Matrices
Chapter: [3] Matrices
Concept: undefined >> undefined
If \[A = \begin{bmatrix}\cos x & \sin x \\ - \sin x & \cos x\end{bmatrix}\] , find x satisfying 0 < x < \[\frac{\pi}{2}\] when A + AT = I
[3] Matrices
Chapter: [3] Matrices
Concept: undefined >> undefined
