Advertisements
Advertisements
प्रश्न
State whether the following statement is True or False:
Inverse of `[(2, 0),(0, 3)]` is `[(1/2, 0),(0, 1/3)]`
पर्याय
True
False
उत्तर
True
APPEARS IN
संबंधित प्रश्न
Find the inverse of the following matrix by elementary row transformations if it exists. `A=[[1,2,-2],[0,-2,1],[-1,3,0]]`
Find the inverse of the matrix `[(1 2 3),(1 1 5),(2 4 7)]` by adjoint method
Find the co-factor of the element of the following matrix:
`[(-1, 2),(-3, 4)]`
Find the adjoint of the following matrix.
`[(2,-3),(3,5)]`
If A = `[(1,-1,2),(3,0,-2),(1,0,3)]` verify that A (adj A) = (adj A) A = | A | I
Find the inverse of the following matrix (if they exist):
`[(2,0,-1),(5,1,0),(0,1,3)]`
Choose the correct answer from the given alternatives in the following question:
If A = `[(lambda,1),(-1, -lambda)]`, and A-1 does not exist if λ = _______
Find the inverse of the following matrices by transformation method:
`[(2, 0, −1),(5, 1, 0),(0, 1, 3)]`
Find the inverse `[(1, 2, 3 ),(1, 1, 5),(2, 4, 7)]` of the elementary row tranformation.
State whether the following is True or False :
A = `[(2, 1),(10, 5)]` is invertible matrix.
State whether the following is True or False :
Singleton matrix is only row matrix.
Check whether the following matrices are invertible or not:
`[(1, 2, 3),(2, 4, 5),(2, 4, 6)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, 0, -1),(5, 1, 0),(0, 1, 3)]`
`cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______
If A = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then |A| |adj A| = ______
If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB
If f(x) = x2 − 2x − 3 then find f(A) when A = `[(1, 2),(2, 1)]`
Find the adjoint of matrix A = `[(2, 0, -1),(3, 1, 2),(-1, 1, 2)]`
The value of Cofactor of element a21 in matrix A = `[(1, 2),(5, -8)]` is ______
Find the inverse of the following matrix:
`[(1,-1),(2,3)]`
If X = `[(8,-1,-3),(-5,1,2),(10,-1,-4)]` and Y = `[(2,1,-1),(0,2,1),(5,p,q)]` then, find p, q if Y = X-1
Solve by matrix inversion method:
3x – y + 2z = 13; 2x + y – z = 3; x + 3y – 5z = - 8
Weekly expenditure in an office for three weeks is given as follows. Assuming that the salary in all the three weeks of different categories of staff did not vary, calculate the salary for each type of staff, using the matrix inversion method.
Week | Number of employees | Total weekly salary (in ₹) |
||
A | B | C | ||
1st week | 4 | 2 | 3 | 4900 |
2nd week | 3 | 3 | 2 | 4500 |
3rd week | 4 | 3 | 4 | 5800 |
adj (AB) is equal to:
The inverse matrix of `((4/5,(-5)/12),((-2)/5,1/2))` is
If A is 3 × 3 matrix and |A| = 4 then |A-1| is equal to:
If A = `[(1,-1),(2,3)]` show that A2 - 4A + 5I2 = 0 and also find A-1.
The matrix M = `[(0,1,2),(1,2,3),(3,1,1)]` and its inverse is N = [nij]. What is the element n23 of matrix N?
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = ______.
If A = `[(2, 2),(4, 5)]` and A–1 = λ(adj(A)), then λ = ______ .
The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible ______.
If A, B are two square matries, such that AB = B, BA = A and n ∈ N then (A + B)n =
If A = `[(x, 1),(1, 0)]` and A = A–1, then x = ______.
Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.
If matrix A = `[(1, -1),(2, 3)]`, then A2 – 4A + 5I is where I is a unit matix.
If A = `[(1, 2),(3, 4)]` verify that A (adj A) = (adj A) A = |A| I