Advertisements
Advertisements
Question
For what value of x, the matrix A = `[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)]` is skew – symmetric
Solution
A = `[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)]`
AT = `[(0, -1, 2),(1, 0, -3),(-2, x^3, 0)]`
The matrix A is skew-symmetric if A = – AT
`[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)] = - [(0, -1, 2),(1, 0, -3),(-2, x^3, 0)]`
`[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)] + [(0, -1, 2),(1, 0, -3),(-2, x^3, 0)] = [(0, 0, 0),(0, 0, 0),(0, 0, 0)]`
`[(0 + 0, 1 - 1, -2 + 2),(-1 + 1, 0 + 0, x^3 - 3),(2 - 2, -3 x^3, 0 + 0)] = [(0, 0, 0),(0, 0, 0),(0, 0, 0)]`
`[(0, 0, 0),(0, 0, x^3 - 3),(0, x^3 - 3, 0)] = [(0, 0, 0),(0, 0, 0),(0, 0, 0)]`
Equating the corresponding entries
x3 – 3 = 0
x3 = 3
⇒ x = `3^(1/3)`
APPEARS IN
RELATED QUESTIONS
Find X and Y if X + Y = `[(7, 0),(3, 5)]` and X – Y = `[(3, 0),(0, 4)]`
If A = `[(0, 4, 9),(8, 3, 7)]`, B = `[(7, 3, 8),(1, 4, 9)]` find the value of B – 5A
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)]`
Solve for x, y : `[(x^2),(y^2)] + 2[(-2x),(-y)] = [(5),(8)]`
Find the order of the product matrix AB if
| (i) | (ii) | (iii) | (iv) | (v) | |
| Order of A | 3 × 3 | 4 × 3 | 4 × 2 | 4 × 5 | 1 × 1 |
| Order of B | 3 × 3 | 3 × 2 | 2 × 2 | 5 × 1 | 1 × 3 |
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 – B)C = AC – BC
If A = `[(costheta, theta),(0, costheta)]`, B = `[(sintheta, 0),(0, sintheta)]` then show that A2 + B2 = I
For the given matrix A = `[(1, 3, 5, 7),(2, 4, 6, 8),(9, 11, 13, 15)]` the order of the matrix AT is
Transpose of a column matrix is
If `cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta[(x, -cos theta),(cos theta, x)]` = I2, find x.
If A = `[(4, 2),(-1, x)]` and such that (A – 2I)(A – 3I) = 0, find the value of x
Show that f(x) f(y) = f(x + y), where f(x) = `[(cosx, -sinx, 0),(sinx, cosx, 0),(0, 0, 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?
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:
`[(4, -2),(3, -5)]`
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:
`[(3, 3, -1),(-2, -2, 1),(-4, -5, 2)]`
Construct the matrix A = [aij]3×3, where aij = 1 – j. State whether A is symmetric or skew–symmetric
A shopkeeper in a Nuts and Spices shop makes gift packs of cashew nuts, raisins and almonds. Pack I contains 100 gm of cashew nuts, 100 gm of raisins and 50 gm of almonds. Pack-II contains 200 gm of cashew nuts, 100 gm of raisins and 100 gm of almonds. Pack-III contains 250 gm of cashew nuts, 250 gm of raisins and 150 gm of almonds. The cost of 50 gm of cashew nuts is ₹ 50, 50 gm of raisins is ₹ 10, and 50 gm of almonds is ₹ 60. What is the cost of each gift pack?
Choose the correct alternative:
If A is skew-symmetric of order n and C is a column matrix of order n × 1, then CT AC is
