Advertisements
Advertisements
प्रश्न
Find the value of x if `[(1, x, 1)] [(1, 3, 2),(2, 5,1),(15, 3, 2)] [(1),(2),(x)]` = 0
उत्तर
Given that `[(1, x, 1)] [(1, 3, 2),(2, 5,1),(15, 3, 2)] [(1),(2),(x)]` = 0
⇒ `[(1 + 2x + 15, 3 + 5x + 3, 2 + x + 2)] [(1),(2),(x)]` = 0
⇒ `[(2x + 16, 5x + 6, x + 4)] [(1),(2),(x)]` = 0
⇒ [2x + 16 + 10x + 12 + x2 + 4x] = 0
⇒ x2 + 16x + 28 = 0
⇒ x2 + 14x + 2x + 28 = 0
⇒ x(x + 14) + 2(x + 14) = 0
⇒ (x + 2)(x + 14) = 0
x + 2 = 0 or x + 14 = 0
∴ x = – 2 or x = – 14
Hence, the values of x are – 2 and – 14.
APPEARS IN
संबंधित प्रश्न
If A and B are square matrices of the same order, then (A + B)(A – B) is equal to ______.
Show that A = `[(5, 3),(-1, -2)]` satisfies the equation A2 – 3A – 7I = O and hence find A–1.
If: `[(2, 1, 3)] [(-1, 0, -1),(-1, 1, 0),(0, 1, 1)] [(1),(0),(-1)]` = A, find A
If A = `[(costheta, sintheta),(-sintheta, costheta)]`, then show that A2 = `[(cos2theta, sin2theta),(-sin2theta, cos2theta)]`
Verify that A2 = I when A = `[(0, 1, -1),(4, -3, 4),(3, -3, 4)]`
Transpose of a column matrix is a column matrix.
If a square matrix A has two identical rows or columns, then det. A is: ____________.
If A `= [(2,1),(-1,2)], "B" = [(1,-2),(2,1)], "C" = [(1,-3),(2,1)],` then ____________.
The value of b for which the function f(x) = x + cos x + b is strictly decreasing over R is:
Amit, Biraj, and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj, and Chirag respectively.
`"A" = [(1,2),(-1,3)] "B" = [(4,0),(1,5)] "C" = [(2,0),(1,-2)]`
If a = 4 and b = -2, based on the above information answer the following:
- Sum of the matrices A, B, and C ,A+(B + C) is ____________.
Amit, Biraj, and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj, and Chirag respectively.
`"A" = [(1,2),(-1,3)] "B" = [(4,0),(1,5)] "C" = [(2,0),(1,-2)]`
If a = 4 and b = -2, based on the above information answer the following:
- `("A"^"T")^"T"` is equal to ____________.
Amit, Biraj, and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj, and Chirag respectively.
`"A" = [(1,2),(-1,3)] "B" = [(4,0),(1,5)] "C" = [(2,0),(1,-2)]`
If a = 4 and b = -2, based on the above information answer the following:
- `("bA")^"T"` is equal to ____________.
Amit, Biraj, and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj, and Chirag respectively.
`"A" = [(1,2),(-1,3)] "B" = [(4,0),(1,5)] "C" = [(2,0),(1,-2)]`
If a = 4 and b = -2, based on the above information answer the following:
- AC - BC is equal to ____________.
Amit, Biraj, and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj, and Chirag respectively.
`"A" = [(1,2),(-1,3)] "B" = [(4,0),(1,5)] "C" = [(2,0),(1,-2)]`
If a = 4 and b = -2, based on the above information answer the following:
- (a + b)B is equal to ____________.
