English

In applying one or more row operations while finding A–1 by elementary row operations, we obtain all zeros in one or more, then A–1 ______. - Mathematics

Advertisements
Advertisements

Question

In applying one or more row operations while finding A–1 by elementary row operations, we obtain all zeros in one or more, then A–1 ______.

Fill in the Blanks

Solution

In applying one or more row operations while finding A–1 by elementary row operations, we obtain all zeros in one or more, then A–1 does not exist.

Explanation:

A–1 does not exist if we apply one or more row operations while finding A–1 by elementary row operations, obtain all zeroes in one or more rows.

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Matrices - Exercise [Page 63]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 3 Matrices
Exercise | Q 81 | Page 63

RELATED QUESTIONS

The cost of 4 pencils, 3 pens and 2 erasers is Rs. 60. The cost of 2 pencils, 4 pens and 6 erasers is Rs. 90 whereas the cost of 6 pencils, 2 pens and 3 erasers is Rs. 70. Find the cost of each item by using matrices.


The sum of three numbers is 6. When second number is subtracted from thrice the sum of first and third number, we get number 10. Four times the sum of third number is subtracted from five times the sum of first and second number, the result is 3. Using above information, find these three numbers by matrix method.


Solve the following equations by the method of reduction :

2x-y + z=1,  x + 2y +3z = 8, 3x + y-4z=1.


For what values of k, the system of linear equations

x + y + z = 2
2x + y – z = 3
3x + 2y + kz = 4

has a unique solution?

 


If `A=|[2,0,-1],[5,1,0],[0,1,3]|` , then find A-1 using elementary row operations


Using elementary transformations, find the inverse of the matrix A =  `((8,4,3),(2,1,1),(1,2,2))`and use it to solve the following system of linear equations :

8x + 4y + 3z = 19

2xyz = 5

x + 2y + 2z = 7


2x − y = 5
4x − 2y = 7


In the following matrix equation use elementary operation R2 → R2 + Rand the equation thus obtained:

\[\begin{bmatrix}2 & 3 \\ 1 & 4\end{bmatrix} \begin{bmatrix}1 & 0 \\ 2 & - 1\end{bmatrix} = \begin{bmatrix}8 & - 3 \\ 9 & - 4\end{bmatrix}\]

If three numbers are added, their sum is 2. If two times the second number is subtracted from the sum of the first and third numbers, we get 8, and if three times the first number is added to the sum of the second and third numbers, we get 4. Find the numbers using matrices. 


Apply the given elementary transformation on each of the following matrices `[(3, -4),(2, 2)]`, R1 ↔ R2.


Apply the given elementary transformation on each of the following matrices `[(2, 4),(1, -5)]`, C1 ↔ C2.


Apply the given elementary transformation on each of the following matrices `[(3, 1, -1),(1, 3, 1),(-1, 1, 3)]`, 3R2 and C2 ↔ C2 – 4C1.


Find the adjoint of the following matrices : `[(2, -3),(3, 5)]`


Choose the correct alternative.

If A = `[(2, 5),(1, 3)]`, then A–1 = _______


Fill in the blank :

Order of matrix `[(2, 1, 1),(5, 1, 8)]` is _______


If three numbers are added, their sum is 2. If 2 times the second number is subtracted from the sum of first and third numbers, we get 8. If three times the first number is added to the sum of second and third numbers, we get 4. Find the numbers using matrices.


State whether the following statement is True or False:

After applying elementary transformation R1 – 3R2 on matrix `[(3, -2),(1, 4)]` we get `[(0, -12),(1, 4)]`


The suitable elementary row transformation which will reduce the matrix `[(1, 0),(2, 1)]` into identity matrix is ______


If A is a 3 × 3 matrix and |A| = 2, then the matrix represented by A (adj A) is equal to. 


If A = `[(a, 0, 0), (0, a, 0), (0, 0, a)]`, then the value of |A| |adj A| is ______ 


If `overlinea = hati + hatj + hatk, overlinea . overlineb = 1` and `overlinea xx overlineb = hatj - hatk,` then `overlineb` = ______ 


If A = `[(1, 1, -1), (1, -2, 1), (2, -1, -3)]`, then (adj A)A = ______


If `[(2, 3), (3, 1)][(x), (y)] = [(-5), (3)]`, then the values of x and y respectively are ______


The inverse of a symmetric matrix is ______.


If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?


Find the values of a and b if A = B, where A = `[("a" + 4, 3"b"),(8, -6)]`, B = `[(2"a" + 2, "b"^2 + 2),(8, "b"^2 - 5"b")]`


Find 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)]`


If possible, find BA and AB, where A = `[(2, 1, 2),(1, 2, 4)]`, B = `[(4, 1),(2, 3),(1, 2)]`


If P = `[(x, 0, 0),(0, y, 0),(0, 0, z)]` and Q = `[("a", 0, 0),(0, "b", 0),(0, 0, "c")]`, prove that PQ = `[(x"a", 0, 0),(0, y"b", 0),(0, 0, z"c")]` = QP


If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (A′)′ = A


If `[(xy, 4),(z + 6, x + y)] = [(8, w),(0, 6)]`, then find values of x, y, z and w.


If A = `[(1, 5),(7, 12)]` and B  `[(9, 1),(7, 8)]`, find a matrix C such that 3A + 5B + 2C is a null matrix.


Find the matrix A such that `[(2, -1),(1, 0),(-3, 4)] "A" = [(-1, -8, -10),(1, -2, -5),(9, 22, 15)]`


Find x, y, z if A = `[(0, 2y, z),(x, y, -z),(x, -y, z)]` satisfies A′ = A–1.


On using elementary column operations C2 → C2 – 2C1 in the following matrix equation `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`, we have: ______.


Two matrices are equal if they have same number of rows and same number of columns.


If (AB)′ = B′ A′, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.


If A = `[(0,0,0,0),(0,0,0,0),(1,0,0,0),(0,1,0,0)],` then ____________.


`abs((1,1,1),("e",0,sqrt2),(2,2,2))` is equal to ____________.


If `[(2, 0, 7),(0, 1, 0),(1, -2, 1)] [(-x, 14x, 7x),(0, 1, 0),(x, -4x, -2x)] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`then find the value of x


If f(x) = `|(1 + sin^2x, cos^2x, 4 sin 2x),(sin^2x, 1 + cos^2x, 4 sin 2x),(sin^2 x, cos^2 x, 1 + 4 sin 2x)|` 

What is the maximum value of f(x)?


if `A = [(2,5),(1,3)] "then" A^-1` = ______


If `[(3,0),(0,2)][(x),(y)] = [(3),(2)], "then"  x = 1  "and"  y = -1`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×