Advertisements
Advertisements
प्रश्न
Find the values of a and b if A = B, where A = `[("a" + 4, 3"b"),(8, -6)]`, B = `[(2"a" + 2, "b"^2 + 2),(8, "b"^2 - 5"b")]`
उत्तर
Given that A = B
⇒ `[("a" + 4, 3"b"),(8, -6)]` = `[(2"a" + 2, "b"^2 + 2),(8, "b"^2 - 5"b")]`
Equating the corresponding elements, we get
a + 4 = 2a + 2
3b = b2 + 2
b2 – 5b = – 6
⇒ 2a – a = 2
b2 – 3b + 2 = 0
b2 – 5b + 6 = 0
∴ a = 2
∴ b2 – 3b + 2 = 0
⇒ b2 – 2b – b + 2 = 0
⇒ b(b – 2) – 1 (b – 2) = 0
⇒ (b – 1)(b – 2) = 0
∴ b = 1, 2
∴ b2 – 5b + 6 = 0
b2 – 3b – 2b + 6 = 0
⇒ b(b – 3) – 2(b – 3) = 0
⇒ (b – 2) (b – 3) = 0
⇒ b = 2, 3
But here 2 is common.
Hence, the value of a = 2 and b = 2.
APPEARS IN
संबंधित प्रश्न
The sum of three numbers is 6. When second number is subtracted from thrice the sum of first and third number, we get number 10. Four times the sum of third number is subtracted from five times the sum of first and second number, the result is 3. Using above information, find these three numbers by matrix method.
Find the inverse of the matrix, `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.
Solve the following equations by the method of reduction :
2x-y + z=1, x + 2y +3z = 8, 3x + y-4z=1.
The sum of three numbers is 9. If we multiply third number by 3 and add to the second number, we get 16. By adding the first and the third number and then subtracting twice the second number from this sum, we get 6. Use this information and find the system of linear equations. Hence, find the three numbers using matrices.
Use elementary column operation C2 → C2 + 2C1 in the following matrix equation :
`[[2,1],[2,0]] = [[3,1],[2,0]] [[1,0],[-1,1]]`
If `A=|[2,0,-1],[5,1,0],[0,1,3]|` , then find A-1 using elementary row operations
Using the properties of determinants, solve the following for x:
`|[x+2,x+6,x-1],[x+6,x-1,x+2],[x-1,x+2,x+6]|=0`
Prove that `|(yz-x^2,zx-y^2,xy-z^2),(zx-y^2,xy-z^2,yz-x^2),(xy-z^2,yz-x^2,zx-y^2)|`is divisible by (x + y + z) and hence find the quotient.
Using properties of determinants, prove that :
`|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc + bc + ca + ab`
The cost of 2 books, 6 notebooks and 3 pens is Rs 40. The cost of 3 books, 4 notebooks and 2 pens is Rs 35, while the cost of 5 books, 7 notebooks and 4 pens is Rs 61. Using this information and matrix method, find the cost of 1 book, 1 notebook and 1 pen separately.
Using elementary row transformations, find the inverse of the matrix A = `[(1,2,3),(2,5,7),(-2,-4,-5)]`
Prove that :
x + y + z + w = 2
x − 2y + 2z + 2w = − 6
2x + y − 2z + 2w = − 5
3x − y + 3z − 3w = − 3
2x − 3z + w = 1
x − y + 2w = 1
− 3y + z + w = 1
x + y + z = 1
2x − y = 5
4x − 2y = 7
Use elementary column operation C2 → C2 + 2C1 in the following matrix equation : \[\begin{bmatrix} 2 & 1 \\ 2 & 0\end{bmatrix} = \begin{bmatrix}3 & 1 \\ 2 & 0\end{bmatrix}\begin{bmatrix}1 & 0 \\ - 1 & 1\end{bmatrix}\]
If three numbers are added, their sum is 2. If two times the second number is subtracted from the sum of the first and third numbers, we get 8, and if three times the first number is added to the sum of the second and third numbers, we get 4. Find the numbers using matrices.
Using elementary row operations, find the inverse of the matrix A = `((3, 3,4),(2,-3,4),(0,-1,1))` and hence solve the following system of equations : 3x - 3y + 4z = 21, 2x -3y + 4z = 20, -y + z = 5.
Apply the given elementary transformation on each of the following matrices `[(3, 1, -1),(1, 3, 1),(-1, 1, 3)]`, 3R2 and C2 ↔ C2 – 4C1.
Find the cofactor matrix, of the following matrices: `[(5, 8, 7),(-1, -2, 1),(-2, 1, 1)]`
Find the adjoint of the following matrices : `[(2, -3),(3, 5)]`
Choose the correct alternative.
If A = `[(2, 5),(1, 3)]`, then A–1 = _______
If three numbers are added, their sum is 2. If 2 times the second number is subtracted from the sum of first and third numbers, we get 8. If three times the first number is added to the sum of second and third numbers, we get 4. Find the numbers using matrices.
Choose the correct alternative:
If A = `[(1, 2),(2, -1)]`, then adj (A) = ______
For which values of xis the matrix
`[(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)]` non-invertible?
If A = `[(a, 0, 0), (0, a, 0), (0, 0, a)]`, then the value of |A| |adj A| is ______
If `overlinea = hati + hatj + hatk, overlinea . overlineb = 1` and `overlinea xx overlineb = hatj - hatk,` then `overlineb` = ______
If AX = B, where A = `[(1, 2, 3), (-1, 1, 2), (1, 2, 4)]` and B = `[(1), (2), (3)]`, then X is equal to ______
If possible, find BA and AB, where A = `[(2, 1, 2),(1, 2, 4)]`, B = `[(4, 1),(2, 3),(1, 2)]`
If P = `[(x, 0, 0),(0, y, 0),(0, 0, z)]` and Q = `[("a", 0, 0),(0, "b", 0),(0, 0, "c")]`, prove that PQ = `[(x"a", 0, 0),(0, y"b", 0),(0, 0, z"c")]` = QP
If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (A′)′ = A
If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (kA)' = (kA')
If A = `[(1, 5),(7, 12)]` and B `[(9, 1),(7, 8)]`, find a matrix C such that 3A + 5B + 2C is a null matrix.
If P(x) = `[(cosx, sinx),(-sinx, cosx)]`, then show that P(x) . (y) = P(x + y) = P(y) . P(x)
If possible, using elementary row transformations, find the inverse of the following matrices
`[(2, -1, 3),(-5, 3, 1),(-3, 2, 3)]`
If possible, using elementary row transformations, find the inverse of the following matrices
`[(2, 3, -3),(-1, 2, 2),(1, 1, -1)]`
If possible, using elementary row transformations, find the inverse of the following matrices
`[(2, 0, -1),(5, 1, 0),(0, 1, 3)]`
If `[(2x + y, 4x),(5x - 7, 4x)] = [(7, 7y - 13),(y, x + 6)]`, then the value of x + y is ______.
If A = `1/pi [(sin^-1(xpi), tan^-1(x/pi)),(sin^-1(x/pi), cot^-1(pix))]`, B = `1/pi [(-cos^-1(x/pi), tan^-1 (x/pi)),(sin^-1(x/pi),-tan^-1(pix))]`, then A – B is equal to ______.
On using elementary column operations C2 → C2 – 2C1 in the following matrix equation `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`, we have: ______.
A matrix denotes a number.
If (AB)′ = B′ A′, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.
`abs((1,1,1),("e",0,sqrt2),(2,2,2))` is equal to ____________.
If f(x) = `|(1 + sin^2x, cos^2x, 4 sin 2x),(sin^2x, 1 + cos^2x, 4 sin 2x),(sin^2 x, cos^2 x, 1 + 4 sin 2x)|`
What is the maximum value of f(x)?
if `A = [(2,5),(1,3)] "then" A^-1` = ______
If `[(3,0),(0,2)][(x),(y)] = [(3),(2)], "then" x = 1 "and" y = -1`
