Advertisements
Advertisements
प्रश्न
Find the adjoint of the following:`1/3[(2, 2, 1),(-2, 1, 2),(1, -2, 2)]`
उत्तर
A = `1/3[(2, 2, 1),(-2, 1, 2),(1, -2, 2)]_(3 xx 3)`
adj (kA) = `"k"^("n" - 1)` adj A
adj A = `(1/3)^2 [(+|(1, 2),(-2, 2)|, -|(-2, 2),(1, 2)|, +|(-2, 1),(1, -2)|),(-|(2, 1),(-2, 2)|, +|(2, 1),(1, 2)|, -|(2, 2),(1, -2)|),(+|(2, 1),(1, 2)|, -|(2, 1),(-2, 2)|, +|(2, 2),(-2, 1)|)]^"T"`
= `1/9[(+(2 + 4), -(-4 - 2), +(4 - 1)),(-4(4 + 2), +(4 - 1), -(-4 - 2)),(+(4 - 1), -(4 + 2), +(2 + 4))]^"T"`
= `1/9[(6, 6, 3),(-6, 3, 6),(, -6, 6)]^"T"`
= `1/9[(6, -6, 3),(6, 3, -6),(3, 6, 6)]`
= `1/3[(2, -2, 1),(2, 1, 2),(1, 2, 2)]`
APPEARS IN
संबंधित प्रश्न
Find the adjoint of the following:
`[(-3, 4),(6,2)]`
Find the adjoint of the following:
`[(2, 3, 1),(3, 4, 1),(3, 7, 2)]`
Find the inverse (if it exists) of the following:
`[(5, 1, 1),(1, 5, 1),(1, 1, 5)]`
Find the inverse (if it exists) of the following:
`[(2, 3, 1),(3, 4, 1),(3, 7, 2)]`
If `"F"(alpha) = [(cosalpha, 0, sinalpha),(0, 1, 0),(-sinalpha, 0, cosalpha)]`, show that `["F"(alpha)]^-1 = "F"(- alpha)`
If A = `[(8, -4),(-5, 3)]`, verify that A(adj A) = (adj A)A = |A|I2
If A = `[(3, 2),(7, 5)]` and B = `[(-1, -3),(5, 2)]`, verify that (AB)–1 = B–1 A–1
If adj(A) = `[(0, -2, 0),(6, 2, -6),(-3, 0, 6)]`, find A–1
A = `[(1, tanx),(-tanx, 1)]`, show that AT A–1 = `[(cos 2x, - sin 2x),(sin 2x, cos 2x)]`
Find the matrix A for which A`[(5, 3),(-1, -2)] = [(14, 7),(7, 7)]`
Given A = `[(1, -1),(2, 0)]`, B = `[(3, -2),(1, 1)]` and C = `[(1, 1),(2, 2)]`, find a martix X such that AXB = C
If A = `[(0, 1, 1),(1, 0, 1),(1, 1, 0)]`, show that `"A"^-1 = 1/2("A"^2 - 3"I")`
Choose the correct alternative:
If A = `[(1, -2),(1, 4)] = [(6, 0),(0, 6)]`, then A =
Choose the correct alternative:
If A = `[(7, 3),(4, 2)]` then 9I2 – A =
Choose the correct alternative:
If A = `[(2, 0),(1, 5)]` and B = `[(1, 4),(2, 0)]` then |adj (AB)| =
Choose the correct alternative:
If A B, and C are invertible matrices of some order, then which one of the following is not true?
Choose the correct alternative:
If A = `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]`, then adj(adj A) is
