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
If \[a, b\] and c are all non-zero and
\[\begin{vmatrix}1 + a & 1 & 1 \\ 1 & 1 + b & 1 \\ 1 & 1 & 1 + c\end{vmatrix} =\] 0, then prove that
\[\frac{1}{a} + \frac{1}{b} + \frac{1}{c} +\]1
= 0
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
If \[\begin{vmatrix}a & b - y & c - z \\ a - x & b & c - z \\ a - x & b - y & c\end{vmatrix} =\] 0, then using properties of determinants, find the value of \[\frac{a}{x} + \frac{b}{y} + \frac{c}{z}\] , where \[x, y, z \neq\] 0
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Find the area of the triangle with vertice at the point:
(3, 8), (−4, 2) and (5, −1)
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Find the area of the triangle with vertice at the point:
(2, 7), (1, 1) and (10, 8)
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Find the area of the triangle with vertice at the point:
(−1, −8), (−2, −3) and (3, 2)
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Find the area of the triangle with vertice at the point:
(0, 0), (6, 0) and (4, 3)
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
