Elementary Transformation of a matrix: The following operation on a matrix are called elementary operations (transformations) 1.The interchange of any two rows (or columns) 2. The multiplication of the elements of any row (or column) by any nonzero number 3. The addition to the elements of any row (or column) the corresponding elements of any other row (or column) multiplied by any number Echelon Form of matrix : A matrix A is said to be in echelon form if (i) every row of A which has all its elements 0, occurs below row, which has a non-zero elements (ii) the first non-zero element in each non –zero row is 1. (iii) The number of zeros before the first non zero elements in a row is less than the number of such zeros in the next now.[ A row of a matrix is said to be a zero row if all its elements are zero]Note: Rank of a matrix does not change by application of any elementary operations For example [(1,1,3),(0,1,2),(0,0,0)],[(1,1,3,6),(0,1,2,2),(0,0,0,0)] are echelon forms The number of non-zero rows in the echelon form of a matrix is defined as its RANK. For example we can reduce the matrixA=[(1,2,3),(2,4,7),(3,6,10)] into echelon form using followingelementary row transformation. (i)R_2 to R_2 -2R_1 and R_3 to R_3 -3R_1 [(1,2,3),(0,0,1),(0,0,1)] (ii)R_2 to R_2 -2R_1 [(1,2,3),(0,0,1),(0,0,0)] This is the echelon form of matrix A Number of nonzero rows in the echelon form =2rArrRank of the matrix A is 2 Rank of the matrix [(1,1,1),(1,-1,-1),(3,1,1)] is :

Elementary Transformation of a matrix: The following operation on a ma

1.	Elementary Transformation of a matrix: The following operation on a matrix are called elementary operations (transformations) 1.The interchange of any two rows (or columns) 2. The multiplication of the elements of any row (or column) by any nonzero number 3. The addition to the elements of any row (or column) the corresponding elements of any other row (or column) multiplied by any number Echelon Form of matrix : A matrix A is said to be in echelon form if (i) every row of A which has all its elements 0, occurs below row, which has a non-zero elements (ii) the first non-zero element in each non –zero row is 1. (iii) The number of zeros before the first non zero elements in a row is less than the number of such zeros in the next now.[ A row of a matrix is said to be a zero row if all its elements are zero]Note: Rank of a matrix does not change by application of any elementary operations For example [(1,1,3),(0,1,2),(0,0,0)],[(1,1,3,6),(0,1,2,2),(0,0,0,0)] are echelon forms The number of non-zero rows in the echelon form of a matrix is defined as its RANK. For example we can reduce the matrixA=[(1,2,3),(2,4,7),(3,6,10)] into echelon form using followingelementary row transformation. (i)R_2 to R_2 -2R_1 and R_3 to R_3 -3R_1 [(1,2,3),(0,0,1),(0,0,1)] (ii)R_2 to R_2 -2R_1 [(1,2,3),(0,0,1),(0,0,0)] This is the echelon form of matrix A Number of nonzero rows in the echelon form =2rArrRank of the matrix A is 2 Rank of the matrix [(1,1,1),(1,-1,-1),(3,1,1)] is :
Answer» 1 2 3 0 Answer :C

Discussion

No Comment Found

Related InterviewSolutions

P (-2,-1) and (0,-3) are the limiting points of a coaxial system of whichC -= x^(2) + y^(2)+ 5x + y + 4 = 0is a member. The circleS -= x^(2) + y^(2) - 4x - 2y - 15 = 0is orthogonal to the circle C . The point where the polar of P cuts the circle S is
Which of the following is/are discontinous at x = 1 ?
Write Minors and Cofactors of the elments of following determinants : |{:(1,0,4),(3,5,-1),(0,1,2):}|
The vertex of the parabola (y-1)^2 =8 (x-1) is at the centre of a circle and the parabola cuts that circle atthe ends of its latusrectum. Then the equation of that circle is
{{:(5x-3y=10),(6y=kx-42):} In the system of linear equations above, k represents a constant. If the system of equations has no solution, what is the value of 2k?
f(x) ={{:(1-sqrt(1-x^(2)),if -1lexle1),(1+ log ""(1)/(x), if xgt1):}
Given that alpha, beta, gamma, delta are in a geometric progression. If alpha, beta are the roots of x^(2)-x+p=0 " and "gamma, delta are the roots of x^(2)-4x+q=0, where p and q are integers, then the ordered pair (p, q) =
A poor , frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately showsthe cost and revenue of his plan. The linear cost function, C(x) , represents the total money spent to make and market the art , while the linear revenue function, R(x) , shows the amount of money he has made in sculpture sales. Fresco initially spent money promoting the project in the media . He also had to pay the celebrities to participate . After 6 months , Fresco had created and sold x number of trash sculptures and finally broke even : he hadn't made or lost any money . How many sculptures did Fresco sell in his first 6 months of the project ?
A poor , frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately showsthe cost and revenue of his plan. The linear cost function, C(x) , represents the total money spent to make and market the art , while the linear revenue function, R(x) , shows the amount of money he has made in sculpture sales. The cost function in the chart is determined by a constant production cost per sculpture - in this case, the amount Fresco pays each celebrity to participate - as well as a fixed cost , or the initial cost of promoting the project . What is the fixed cost of Fresco's trash sculpture project ?
An ellipse is incribed in a rectangle and if the angle between the diagonals is tan ^(-1)2sqrt2then e=

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment