Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
A = diag [2 –3 –5]
∴ A = `[(2, 0, 0),(0, -3, 0),(0, 0, -5)]`
B = diag [4 –6 –3]
∴ B = `[(4, 0, 0),(0, -6, 0),(0, 0, -3)]`
C = diag [–3 4 1]
∴ C = `[(-3, 0, 0),(0, 4, 0),(0, 0, 1)]`
2A + B – 5C = 2 diag [2 – 3 – 5] + diag [4 – 6 – 3] – 5 diag [ –3 4 1]
`= 2[(2, 0, 0),(0, -3, 0),(0, 0, -5)] + [(4, 0, 0),(0, -6, 0),(0, 0, -3)] -5[(-3, 0, 0),(0, 4, 0),(0, 0, 1)]`
`= [(4, 0, 0),(0, -6, 0),(0, 0, -10)] + [(4, 0, 0),(0, -6, 0),(0, 0, -3)] - [(-15, 0, 0),(0, 20, 0),(0, 0, 5)]`
`= [(4 + 4 - (-15), 0, 0),(0, -6 - 6 - 20, 0),(0, 0, -10 - 3 - 5)]`
`= [(23, 0, 0),(0, -32, 0),(0, 0, -18)]`
= diag [23 – 32 – 18].
APPEARS IN
संबंधित 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.
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 x, y, and z from the following equation:
`[(4,3),(x,5)] = [(y,z),(1,5)]`
`A = [a_(ij)]_(mxxn)` is a square matrix, if ______.
Let A = `[(0,1),(0,0)]`show that (aI+bA)n = anI + nan-1 bA , where I is the identity matrix of order 2 and n ∈ N
If A is a square matrix such that A2 = A, then (I + A)3 – 7 A is equal to ______.
In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.
Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.
Investigate for what values of λ and μ the equations
2x + 3y + 5z = 9
7x + 3y - 2z = 8
2x + 3y + λz = μ have
A. No solutions
B. Unique solutions
C. An infinite number of solutions.
If\[A = \begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}\]prove that A − AT is a skew-symmetric matrix.
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
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:
`[(3, -2, 4),(0, 0, -5),(0, 0, 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:
`[(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:
`[(5),(4),(-3)]`
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:
`[(6, 0),(0, 6)]`
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?
`[(7, 5),(-4, 7)]`
Find k if the following matrix is singular:
`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A2 – 4A is a scalar matrix
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 _______
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
State whether the following statement is True or False:
If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2
If A = `[(1, 3, 3),(3, 1, 3),(3, 3, 1)]`, then show that A2 – 5A is a scalar matrix
If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2
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)]`
A square matrix A = [aij]nxn is called a diagonal matrix if aij = 0 for ____________.
If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.
The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.
The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]` is a ____________.
If A is a square matrix such that A2 = A, then (I + A)2 - 3A is ____________.
If a matrix A is both symmetric and skew symmetric then matrix A is ____________.
`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?
A = `[a_(ij)]_(m xx n)` is a square matrix, if
The minimum number of zeros in an upper triangular matrix will be ______.
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 ______.
