Advertisements
Advertisements
प्रश्न
If A is a square matrix, such that A2=A, then write the value of 7A−(I+A)3, where I is an identity matrix.
Advertisements
उत्तर
7A−(I+A)3=7A−[I3+A3+3⋅I2⋅A+3⋅I⋅A2]
=7A−(I+A3+3A+3A2)
=7A−(I+A2⋅A+3A+3A2)
=7A−(I+A⋅A+3A+3A) (∵A2=A)
=7A−(I+A2+6A)
=7A−(I+A+6A)
=7A−(I+7A)
=7A−I−7A
=−I
∴ 7A−(I+A)3=−I
APPEARS IN
संबंधित प्रश्न
Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
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:
`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]`
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:
`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
Identify the following matrix is singular or non-singular?
`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`
Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.
Construct the matrix A = [aij]3 × 3 where aij = i − j. State whether A is symmetric or skew-symmetric.
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 = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix
Choose the correct alternative:
If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______
State whether the following statement is True or False:
If `[(3, 0),(0, 2)][(x),(y)] = [(3),(2)]`, then x = 1 and y = – 1
If A is a square matrix of order 2 such that A(adj A) = `[(7, 0),(0, 7)]`, then |A| = ______
The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.
If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
2X + 3Y = `[(2, 3),(4, 0)]`, 3Y + 2Y = `[(-2, 2),(1, -5)]`
For any square matrix A, AAT is a ____________.
If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.
The matrix A `=[(0,1),(1,0)]` is a ____________.
`root(3)(4663) + 349` = ? ÷ 21.003
A matrix is said to be a column matrix if it has
A matrix is said to be a row matrix, if it has
A square matrix B = [bÿ] m × m is said to be a diagonal matrix if all diagonal elements are
If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to
If the sides a, b, c of ΔABC satisfy the equation 4x3 – 24x2 + 47x – 30 = 0 and `|(a^2, (s - a)^2, (s - a)^2),((s - b)^2, b^2, (s - b)^2),((s - c)^2, (s - c)^2, c^2)| = p^2/q` where p and q are co-prime and s is semiperimeter of ΔABC, then the value of (p – q) is ______.
If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.
If A = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.
A matrix which is both symmetric and skew symmetric matrix is a ______.
Matrices are classified into different types based on which two features?
Which elements form the diagonal of a square matrix?
An identity matrix (unit matrix) is a square matrix with:
