Advertisements
Advertisements
Question
If A = `[(sec60°, cos90°),(-3tan45°, sin90°)] and "B" = [(0, cos45°),(-2, 3sin90°)]` Find : A2
Solution
Given
A = `[(sec60°, cos90°),(-3tan45°, sin90°)]`
and
B = `[(0, cos45°),(-2, 3sin90°)]`
A = `[(sec60° , cos90°),(-3tan45°, sin90°)] = [(2, 0),(3, 1)]` ...(∵ sec60° = 2, cos90° = 0, tan45° = 1, sin90° = 1)
B = `[(0, cos45°),(-2, 3sin90°)] = [(0, 1),(-2, 3)]` ...(∵ cot45° = 1)
A2 = A x A = `[(2, 0),(-3, 1)][(2, 0),(-3, 1)]`
= `[(4 + 0, 0 + 0),(-6 - 3, 0 + 1)]`
= `[(4, 0),(-9, 1)]`.
APPEARS IN
RELATED QUESTIONS
Given `[(2, 1),(-3,4)]` . X = `[(7),(6)]`. Write:
- the order of the matrix X.
- the matrix X.
If A = `[(2, 5),(1, 3)]`, B = `[(4, -2),(-1, 3)]` and I is the identity matric of the same order and At is the transpose of matrix A, find At.B + BI.
Evaluate:
`3[(5, -2)]`
If A = `[(2, 1),(1, 3)]` and B = `[(3),(-11)]`, find the matrix X such that AX = B.
If `A = [(2, 5),(1, 3)]`, `B = [(4, -2),(-1, 3)]` and I is Identity matrix of same order and `A^t` is the transpose of matrix A find `A^t.B + BI`
Given A = `[(p, 0),(0, 2)]`, B = `[(0, -q),(1, 0)]`, C = `[(2, -2),(2, 2)]` and BA = C2. Find the values of p and q.
If A = `[(3, 7),(2, 4)]`, B = `[(0, 2),(5, 3)]` and C = `[(1, -5),(-4, 6)]`. Find AB – 5C.
Given matrix A = `[(4sin30^@,cos0^@), (cos0^@,4sin30^@)] and B = [(4), (5)]` If AX = B.
Write the order of matrix X.
If `"A" = [(3 , 1),(2 , 1)] and "B" = [(1 , -2),(5 , 3)]`, then show that (A - B)2 ≠ A2 - 2AB + B2.
If A = `[(3, -4),(-1, 2)]`, find matrix B such that BA = I,where I is unity matrix of order 2
