Advertisements
Advertisements
प्रश्न
Find the matrix A which satisfies the matrix relation `"A"= [(1, 2, 3),(4, 5, 6)] = [(-7, -8, -9),(2, 4, 6)]`
उत्तर
`"A"= [(1, 2, 3),(4, 5, 6)] = [(-7, -8, -9),(2, 4, 6)]` ......(1)
(2 × 2)(2 × 3) = 2 × 3
∴ A must be a 2 × 2 matrix.
Let A = `[(x, y),(z, "t")]`
`[(x, y),(z, "t")] [(1, 2, 3),(4, 5, 6)] = [(x + 4y, 2x + 5y, 3x + 6),(z + 4"t", 2z + 5"t", 3z + 6"t")]`
Using eqation (1) we have
`[(x + 4y, 2x + 5y, 3x + 6),(z + 4"t", 2z + 5"t", 3z + 6"t")] = [(-7, -8, -9),(2, 4, 6)]`
Equating the line entries
x + 4y = – 7 .......(1)
2x + 5y = – 8 ......(2)
3x + 6y = – 9 ......(3)
z + 4t = 2 .......(4)
2z + 5t = 4 ......(5)
3z + 6t = 6 .......(6)
(1) × 2 ⇒ 2x + 8y = – 14
(2) ⇒ 2x + 5y = – 8
0 + 3y = – 6
y = `- 6/3`
= – 2
Substituting for y in equation (1)
(1) ⇒ x + 4 × – 2 = – 7
× – 8 = – 7
x = 8 – 7 = 1
(4) × 2 ⇒ 2z + 8t = 4
(4) ⇒ 2z + 5t = 4
– ing 0 + 3t = 0
t = `0/3`
= 0
Substituting for t in equation (4)
(4) ⇒ z + 4 × 0 = 2
z = 2
∴ The required matrix A is A = `[(1, -2),(2, 0)]`
APPEARS IN
संबंधित प्रश्न
In the matrix A = `[(8, 9, 4, 3),(- 1, sqrt(7), sqrt(3)/2, 5),(1, 4, 3, 0),(6, 8, -11, 1)]`, Write the elements a22, a23, a24, a34, a43, a44
If A = `[(5, 4, 3),(1, -7, 9),(3, 8, 2)]` then find the transpose of A
If A = `[(5, 2, 2),(-sqrt(17), 0.7, 5/2),(8, 3, 1)]` then verify (AT)T = A
Find the non-zero values of x satisfying the matrix equation
`x[(2x, 2),(3, x)] + 2[(8, 5x),(4, 4x)] = 2[(x^2 + 8, 24),(10, 6x)]`
A has ‘a’ rows and ‘a + 3’ columns. B has ‘b’ rows and ‘17 − b’ columns, and if both products AB and BA exist, find a, b?
Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that A(BC) = (AB)C
If A = `[(3, 1),(-1, 2)]` show that A2 – 5A + 7I2 = 0
Transpose of a column matrix is
A = `[(3, 0),(4, 5)]`, B = `[(6, 3),(8, 5)]`, C = `[(3, 6),(1, 1)]` find the matrix D, such that CD – AB = 0
Determine the value of x + y if `[(2x + y, 4x),(5x - 7, 4x)] = [(7, 7y - 13),(y, x + 6)]`
Verify the property A(B + C) = AB + AC, when the matrices A, B, and C are given by A = `[(2, 0, -3),(1, 4, 5)]`, B = `[(3, 1),(-1, 0),(4, 2)]` and C = `[(4, 7),(2, 1),(1,-1)]`
If A is a 3 × 4 matrix and B is a matrix such that both ATB and BAT are defined, what is the order of the matrix B?
If `[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)]` is skew – symmetric find the values of p, q and r
Choose the correct alternative:
If A = `[(1, 2, 2),(2, 1, -2),("a", 2, "b")]` is a matrix satisfying the equation AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to
Choose the correct alternative:
If the points (x, – 2), (5, 2), (8, 8) are collinear, then x is equal to
Let det M denotes the determinant of the matrix M. Let A and B be 3 × 3 matrices with det A = 3 and det B = 4. Then the det (2AB) is
Let A = `[(cosα, -sinα),(sinα, cosα)]`, α ∈ R such that A32 = `[(0, -1),(1, 0)]`. Then a value of α is ______.
Let (p1, q1, r1) and (p2, q2, r2) are satisfying `|(1, p, p^2),(1, q, q^2),(1, r, r^2)|` = 6 (where pi, qi ri ∈ N and pi < qi < ri and i = 1, 2) and point (p1, q1, r1) lies on the plane 2x + 3y + 6z = k, and point (p2, q2, r2) lies on the plane 2x + 3y + 6z = k2 (where p1 = p2 = 1) If distance between these planes is 'd', then value of (210d) is ______.
