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 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.
Find the value of x, y and z from the following equation:
`[(x + y, 2),(5 + z, xy)] = [(6, 2), (5, 8)]`
Find the value of a, b, c and d from the equation:
`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`
`A = [a_(ij)]_(m xx n)` 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 = `[(α, β),(γ, -α)]` is such that A2 = I, then ______.
Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.
If 𝒙 = r cos θ and y= r sin θ prove that JJ-1=1.
Find the non-singular matrices P & Q such that PAQ is in normal form where`[(1,2,3,4),(2,1,4,3),(3,0,5,-10)]`
If li, mi, ni, i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where \[A = \begin{bmatrix}l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ l_3 & m_3 & n_3\end{bmatrix}\]
Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`
if `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`
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:
`[(3, 0, 0),(0, 5, 0),(0, 0, 1/3)]`
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:
`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
Identify the following matrix is singular or non-singular?
`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`
Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is unit matrix of order 2
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, 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
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 = ______
AB = AC ⇒ B = C for any three matrices of same order.
If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2
For any square matrix A, AAT is a ____________.
If A is a square matrix such that A2 = A, then (I + A)2 - 3A is ____________.
A matrix is said to be a column matrix if it has
A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an
The minimum number of zeros in an upper triangular matrix will be ______.
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 ______.
If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.
