Advertisements
Advertisements
प्रश्न
If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (AT)T.
Advertisements
उत्तर
A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`
∴ AT = `[(7, -2, 5),(3, -4, 9),(1, 1, 1)]`
∴ (AT)T = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`.
APPEARS IN
संबंधित प्रश्न
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |A|
Find the value of a, b, c and d from the equation:
`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`
If A = `[(0, -tan α/2), (tan α/2, 0)]` and I is the identity matrix of order 2, show that I + A = `(I - A)[(cos α, -sin α),(sin α, cos α)]`
If 𝒙 = r cos θ and y= r sin θ prove that JJ-1=1.
If li, mi, ni, i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where \[A = \begin{bmatrix}l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ l_3 & m_3 & n_3\end{bmatrix}\]
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
Choose the correct alternative.
The matrix `[(8, 0, 0),(0, 8, 0),(0, 0, 8)]` is _______
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(0, 4, 7),(-4, 0, -3),(-7, 3, 0)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[9 sqrt(2) -3]`
Identify the following matrix is singular or non-singular?
`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
Find k if the following matrix is singular:
`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
If A = `[(5, 1, -1),(3, 2, 0)]`, Find (AT)T.
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
Select the correct option from the given alternatives:
Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______
Select the correct option from the given alternatives:
If A and B are square matrices of equal order, then which one is correct among the following?
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find 2A + B – 5C
Answer the following question:
If A = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)]`, B = `[(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`, show that AB and BA are both singular matrices
State whether the following statement is True or False:
If A is non singular, then |A| = 0
Show by an example that for A ≠ O, B ≠ O, AB = O
For any square matrix A, AAT is a ____________.
If a matrix A is both symmetric and skew-symmetric, then ____________.
If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.
A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an
A = `[a_(ij)]_(m xx n)` is a square matrix, if
How many matrices can be obtained by using one or more numbers from four given numbers?
If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.
Let A = `[(0, -2),(2, 0)]`. If M and N are two matrices given by M = `sum_(k = 1)^10 A^(2k)` and N = `sum_(k = 1)^10 A^(2k - 1)` then MN2 is ______.
If A = `[(0, -tan θ/2),(tan θ/2, 0)]` and (I2 + A) (I2 – A)–1 = `[(a, -b),(b, a)]` then 13(a2 + b2) is equal to ______.
Matrices are classified into different types based on which two features?
A matrix with only one column is called a:
What is the order of a column matrix with \[m\] rows?
A matrix where the number of rows equals the number of columns is called a:
If \[m=n\], what type and order does the matrix have?
A diagonal matrix is a square matrix in which:
Which condition holds for a diagonal matrix when \[i\ne j\]?
Which pair of conditions defines a scalar matrix?
Which statement correctly describes the relationship between scalar matrices and diagonal matrices?
Which matrix is an identity matrix?
