Advertisements
Advertisements
प्रश्न
If: `[(2, 1, 3)] [(-1, 0, -1),(-1, 1, 0),(0, 1, 1)] [(1),(0),(-1)]` = A, find A
उत्तर
We have, `[(2, 1, 3)]_(1 xx 3) [(-1, 0, -1),(-1, 1, 0),(0, 1, 1)]_(3 xx 3) [(1),(0),(-1)]_(3 xx 1)` = A
∴ `[(2, 1, 3)]_(1 xx 3) [(-1 + 0 + 1),(-1 + 0 + 0),(0 + 0 - 1)]_(3 xx 1)` = A
⇒ `[(2, 1, 3)]_(1 xx 3) [(0),(-1),(-1)]_(3 xx 1)`` = A
⇒ `[0 -1 -3]` = A
⇒ A = [– 4]
APPEARS IN
संबंधित प्रश्न
If A and B are square matrices of the same order, then (A + B)(A – B) is equal to ______.
Find the value of x if `[(1, x, 1)] [(1, 3, 2),(2, 5,1),(15, 3, 2)] [(1),(2),(x)]` = 0
Show that A = `[(5, 3),(-1, -2)]` satisfies the equation A2 – 3A – 7I = O and hence find A–1.
If A = `[(costheta, sintheta),(-sintheta, costheta)]`, then show that A2 = `[(cos2theta, sin2theta),(-sin2theta, cos2theta)]`
Verify that A2 = I when A = `[(0, 1, -1),(4, -3, 4),(3, -3, 4)]`
Transpose of a column matrix is a column matrix.
If a square matrix A has two identical rows or columns, then det. A is: ____________.
If A `= [(2,1),(-1,2)], "B" = [(1,-2),(2,1)], "C" = [(1,-3),(2,1)],` then ____________.
Amit, Biraj, and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj, and Chirag respectively.
`"A" = [(1,2),(-1,3)] "B" = [(4,0),(1,5)] "C" = [(2,0),(1,-2)]`
If a = 4 and b = -2, based on the above information answer the following:
- Sum of the matrices A, B, and C ,A+(B + C) is ____________.
Amit, Biraj, and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj, and Chirag respectively.
`"A" = [(1,2),(-1,3)] "B" = [(4,0),(1,5)] "C" = [(2,0),(1,-2)]`
If a = 4 and b = -2, based on the above information answer the following:
- `("A"^"T")^"T"` is equal to ____________.
Amit, Biraj, and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj, and Chirag respectively.
`"A" = [(1,2),(-1,3)] "B" = [(4,0),(1,5)] "C" = [(2,0),(1,-2)]`
If a = 4 and b = -2, based on the above information answer the following:
- `("bA")^"T"` is equal to ____________.
Amit, Biraj, and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj, and Chirag respectively.
`"A" = [(1,2),(-1,3)] "B" = [(4,0),(1,5)] "C" = [(2,0),(1,-2)]`
If a = 4 and b = -2, based on the above information answer the following:
- (a + b)B is equal to ____________.
