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प्रश्न
A matrix denotes a number.
पर्याय
True
False
उत्तर
This statement is False.
Explanation:
A matrix is an array of elements, numbers or functions having rows and columns.
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संबंधित प्रश्न
Find the inverse of the matrix, `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.
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.
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 elementary transformations, find the inverse of the matrix A = `((8,4,3),(2,1,1),(1,2,2))`and use it to solve the following system of linear equations :
8x + 4y + 3z = 19
2x + y + z = 5
x + 2y + 2z = 7
Using properties of determinants, prove that :
`|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc + bc + ca + ab`
Prove that :
2x − 3z + w = 1
x − y + 2w = 1
− 3y + z + w = 1
x + y + z = 1
2x − y = 5
4x − 2y = 7
In the following matrix equation use elementary operation R2 → R2 + R1 and the equation thus obtained:
Use elementary column operations \[C_2 \to C_2 - 2 C_1\] in the matrix equation \[\begin{pmatrix}4 & 2 \\ 3 & 3\end{pmatrix} = \begin{pmatrix}1 & 2 \\ 0 & 3\end{pmatrix}\begin{pmatrix}2 & 0 \\ 1 & 1\end{pmatrix}\] .
Apply the given elementary transformation on each of the following matrices `[(2, 4),(1, -5)]`, C1 ↔ C2.
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 = _______
Fill in the blank :
Order of matrix `[(2, 1, 1),(5, 1, 8)]` is _______
State whether the following is True or False :
Single element matrix is row as well as column matrix.
Solve the following :
If A = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`, the reduce it to unit matrix by using row transformations.
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) = ______
Find the inverse of matrix A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)]` by using elementary row transformations
The cofactors of the elements of the first column of the matrix A = `[(2,0,-1),(3,1,2),(-1,1,2)]` are ______.
If `overlinea = hati + hatj + hatk, overlinea . overlineb = 1` and `overlinea xx overlineb = hatj - hatk,` then `overlineb` = ______
Let F(α) = `[(cosalpha, -sinalpha, 0), (sinalpha, cosalpha, 0), (0, 0, 1)]` where α ∈ R. Then [F(α)]-1 is equal to ______
If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?
In the matrix A = `[("a", 1, x),(2, sqrt(3), x^2 - y),(0, 5, (-2)/5)]`, write: elements a23, a31, a12
Construct a 3 × 2 matrix whose elements are given by aij = ei.x sinjx.
Find non-zero values of x satisfying the matrix equation:
`x[(2x, 2),(3, x)] + 2[(8, 5x),(4, 4x)] = 2[(x^2 + 8, 24),(10, 6x)]`
If possible, find BA and AB, where A = `[(2, 1, 2),(1, 2, 4)]`, B = `[(4, 1),(2, 3),(1, 2)]`
If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (A′)′ = (AB)' = B'A'
If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (kA)' = (kA')
If `[(xy, 4),(z + 6, x + y)] = [(8, w),(0, 6)]`, then find values of x, y, z and w.
Find the values of a, b, c and d, if `3[("a", "b"),("c", "d")] = [("a", 6),(-1, 2"d")] + [(4, "a" + "b"),("c" + "d", 3)]`
If P(x) = `[(cosx, sinx),(-sinx, cosx)]`, then show that P(x) . (y) = P(x + y) = P(y) . P(x)
Find x, y, z if A = `[(0, 2y, z),(x, y, -z),(x, -y, z)]` satisfies A′ = A–1.
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)]`
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: ______.
On using elementary row operation R1 → R1 – 3R2 in the following matrix equation: `[(4, 2),(3, 3)] = [(1, 2),(0, 3)] [(2, 0),(1, 1)]`, we have: ______.
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.
If A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`, then AB and BA are defined and equal.
If `[(2, 0, 7),(0, 1, 0),(1, -2, 1)] [(-x, 14x, 7x),(0, 1, 0),(x, -4x, -2x)] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`then find the value of x
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)?
