Mathematics Problems

Show that the transformation y_1=2x+y+z ; y_2=x+y+2z; y_3=x-2z is regular. Write down the inverse transformation Question Question Show that the transformation y_1=2x+y+z ; y_2=x+y+2z; y_3=x-2z is regular. Write down the inverse transformation Topic Linear Transformation Linear Transformation Problems Show that the transformation y_1=x_1+2x_2+5x_3 ; y_2=2x_1+4x_2+11x_3 ; y_3= -2x_2+2x_3 is regular. Write down the inverse transformation Show that the transformation y_1=2x-2y-z ; y_2= - 4x+5y+3z ; y_3=x-y-z is regular and find out the Inverse transformation. Show that the transformation y_1=2x+y+z ;…

Show that the transformation y_1=2x-2y-z ; y_2= - 4x+5y+3z ; y_3=x-y-z is regular and find out the Inverse transformation. Question Question Show that the transformation y_1=2x-2y-z ; y_2= - 4x+5y+3z ; y_3=x-y-z is regular and find out the Inverse transformation. Topic Linear Transformation Linear Transformation Problems Show that the transformation y_1=x_1+2x_2+5x_3 ; y_2=2x_1+4x_2+11x_3 ; y_3= -2x_2+2x_3 is regular. Write down the inverse transformation Show that the transformation y_1=2x-2y-z ; y_2= - 4x+5y+3z ; y_3=x-y-z is regular and find out the…

Show that the transformation y_1=x_1+2x_2+5x_3 ; y_2=2x_1+4x_2+11x_3 ; y_3= -2x_2+2x_3 is regular. Write down the inverse transformation Question Question Show that the transformation y_1=x_1+2x_2+5x_3 ; y_2=2x_1+4x_2+11x_3 ; y_3= -2x_2+2x_3 is regular. Write down the inverse transformation Topic Linear Transformation Linear Transformation Problems Show that the transformation y_1=x_1+2x_2+5x_3 ; y_2=2x_1+4x_2+11x_3 ; y_3= -2x_2+2x_3 is regular. Write down the inverse transformation Show that the transformation y_1=2x-2y-z ; y_2= - 4x+5y+3z ; y_3=x-y-z is regular and find out the Inverse transformation. Show that…

Reduce the Quadratic form 3x^2+5y^2+3z^2-2yz+2zx-2xy to the Canonical form Question Question Reduce the Quadratic form 3x^2+5y^2+3z^2-2yz+2zx-2xy to the Canonical form Topic Orthogonal Transformation Problems Reduce 8x^2+7y^2+3z^2-12xy+4xz-8yz into canonical form using orthogonal transformation. Also indicate the nature, index, rank and signature of the quadratic form Reduce the Quadratic form 3x^2+5y^2+3z^2-2yz+2zx-2xy to the Canonical form  

Reduce 8x^2+7y^2+3z^2-12xy+4xz-8yz into canonical form using orthogonal transformation. Question Question Reduce 8x^2+7y^2+3z^2-12xy+4xz-8yz into canonical form using orthogonal transformation. Also indicate the nature, index, rank and signature of the quadratic form Topic Orthogonal Transformation Problems Reduce 8x^2+7y^2+3z^2-12xy+4xz-8yz into canonical form using orthogonal transformation Reduce the Quadratic form 3x^2+5y^2+3z^2-2yz+2zx-2xy to the Canonical form  

Using Rayleigh' s power method find numerically the largest Eigen value and corresponding Eigen vector of the matrix, A=[(25,1,2,),(1,3,0),(2,0,-4)] Question Question Using Rayleigh' s power method find numerically the largest Eigen value and corresponding Eigen vector of the matrix, A=[(25,1,2,),(1,3,0),(2,0,-4)] Topic Rayleigh's Power Method Rayleigh's Power Method Problems Find the largest Eigen value and the corresponding Eigen vector of the matrix by the power method given that A =[(2,0,1),(0,2,0),(1,0,2)] Find the dominant Eigen value and the corresponding Eigen vector of…

Find the numerically largest Eigen value and the corresponding Eigen vector of matrix A = [(4,1,-1),(2,3,-1),(-2,1,5)] by taking the initial approximation to the Eigen vector as [1, 0.8,-0.8] ^T. Perform 5 iterations Question Question Find the numerically largest Eigen value and the corresponding Eigen vector of matrix A = [(4,1,-1),(2,3,-1),(-2,1,5)] by taking the initial approximation to the Eigen vector as [1, 0.8,-0.8] ^T. Perform 5 iterations Topic Rayleigh's Power Method Rayleigh's Power Method Problems Find the largest Eigen value and…

Find the largest Eigen value and the corresponding Eigen vector of the matrix A=[(2,-1,0),(-1,2,-1),(0,-1,2) by using power by method taking the initial vector as [1, 1, 1]^T Question Question Find the largest Eigen value and the corresponding Eigen vector of the matrix A=[(2,-1,0),(-1,2,-1),(0,-1,2) by using power by method taking the initial vector as [1, 1, 1]^T Topic Rayleigh's Power Method Rayleigh's Power Method Problems Find the largest Eigen value and the corresponding Eigen vector of the matrix by the power…

Find the dominant Eigen value and the corresponding Eigen vector of the matrix A=[(6,-2,2),((-2,3,-1),(2,-1,3)] by power method taking the initial Eigen vector as [1,1,1] Question Question Find the dominant Eigen value and the corresponding Eigen vector of the matrix A=[(6,-2,2),((-2,3,-1),(2,-1,3)] by power method taking the initial Eigen vector as [1,1,1] Topic Rayleigh's Power Method Rayleigh's Power Method Problems Find the largest Eigen value and the corresponding Eigen vector of the matrix by the power method given that A =[(2,0,1),(0,2,0),(1,0,2)] Find…

Find the largest Eigen value and the corresponding Eigen vector of the matrix by the power method given that A =[(2,0,1),(0,2,0),(1,0,2)] Question Question Find the largest Eigen value and the corresponding Eigen vector of the matrix by the power method given that A =[(2,0,1),(0,2,0),(1,0,2)] Topic Rayleigh's Power Method Rayleigh's Power Method Problems Find the largest Eigen value and the corresponding Eigen vector of the matrix by the power method given that A =[(2,0,1),(0,2,0),(1,0,2)] Find the dominant Eigen value and the…

Diagonalize the matrix [(1,1),(3,-1)] Question Question Diagonalize the matrix [(1,1),(3,-1)] Topic Diagonalisation of a Square Matrix Related Problems Reduce the matrix A=[(-1,3),(-2,4)] to the diagonal form Diagonalize the matrix [(-19,7),(-42,16)] Reduce the matrix A=[(5,4),(1,2)] into the diagonal form Diagonalize the matrix [(1,1),(3,-1)]

Reduce the matrix A=[(5,4),(1,2)] into the diagonal form Question Question Reduce the matrix A=[(5,4),(1,2)] into the diagonal form Topic Diagonalisation of a Square Matrix Related Problems Reduce the matrix A=[(-1,3),(-2,4)] to the diagonal form Diagonalize the matrix [(-19,7),(-42,16)] Reduce the matrix A=[(5,4),(1,2)] into the diagonal form Diagonalize the matrix [(1,1),(3,-1)]

Diagonalize the matrix [(-19,7),(-42,16)] Question Question Diagonalize the matrix [(-19,7),(-42,16)] Topic Diagonalisation of a Square Matrix Related Problems Reduce the matrix A=[(-1,3),(-2,4)] to the diagonal form Diagonalize the matrix [(-19,7),(-42,16)] Reduce the matrix A=[(5,4),(1,2)] into the diagonal form Diagonalize the matrix [(1,1),(3,-1)]

Reduce the matrix A=[(-1,3),(-2,4)] to the diagonal form Question Question Reduce the matrix A=[(-1,3),(-2,4)] to the diagonal form Topic Diagonalisation of a Square Matrix Related Problems Reduce the matrix A=[(-1,3),(-2,4)] to the diagonal form Diagonalize the matrix [(-19,7),(-42,16)] Reduce the matrix A=[(5,4),(1,2)] into the diagonal form Diagonalize the matrix [(1,1),(3,-1)]

Solve the equation by Gauss Siedal method 10x+2y+z=9 ; x+10y-z=-22 ; -2x+3y+10z=22 Question Question Solve the equation by Gauss Siedal method 10x+2y+z=9 ; x+10y-z=-22 ; -2x+3y+10z=22 Topic Gauss elimination method, Gauss Jordan method, Gauss Siedal method Gauss elimination method problems Solve by Gauss elimination method 2x+y+4z=12; 4x+11y-z=33; 8x-3y+2z=20 Solve the following equations by Gauss elimination method x+2y+z=3; 2x+3y+2z=5; 3x-5y+5z=2 Solve the following system of equations by Gauss elimination method x_1+x_2+x_3+x_4=2; 2x_1-x_2+2x_3-x_4=-5; 3x_1+2x_2+3x_3+4x_4=7; x_1-2x_2-3x-3+2x_4=5; Solve by Gauss Elimination method x_1-2x_2+3x_3=2 ;…

Solve the equation by Gauss Siedal method (Carry out 3 Iterations) 20x+y-2z=17 ; 3x+20y-z=-18 ; 2x-3y+20z=25 Question Question Solve the equation by Gauss Siedal method (Carry out 3 Iterations) 20x+y-2z=17 ; 3x+20y-z=-18 ; 2x-3y+20z=25 Topic Gauss elimination method, Gauss Jordan method, Gauss Siedal method Gauss elimination method problems Solve by Gauss elimination method 2x+y+4z=12; 4x+11y-z=33; 8x-3y+2z=20 Solve the following equations by Gauss elimination method x+2y+z=3; 2x+3y+2z=5; 3x-5y+5z=2 Solve the following system of equations by Gauss elimination method x_1+x_2+x_3+x_4=2; 2x_1-x_2+2x_3-x_4=-5; 3x_1+2x_2+3x_3+4x_4=7;…

Solve the system of equation by Gauss Siedal method 83x+11y-4z=95 ; 7x+52y+13z=104 ; 3x+8y+29z=71 Question Question Solve the system of equation by Gauss Siedal method 83x+11y-4z=95 ; 7x+52y+13z=104 ; 3x+8y+29z=71 Topic Gauss elimination method, Gauss Jordan method, Gauss Siedal method Gauss elimination method problems Solve by Gauss elimination method 2x+y+4z=12; 4x+11y-z=33; 8x-3y+2z=20 Solve the following equations by Gauss elimination method x+2y+z=3; 2x+3y+2z=5; 3x-5y+5z=2 Solve the following system of equations by Gauss elimination method x_1+x_2+x_3+x_4=2; 2x_1-x_2+2x_3-x_4=-5; 3x_1+2x_2+3x_3+4x_4=7; x_1-2x_2-3x-3+2x_4=5; Solve by Gauss…

Solve the following system of equations by Gauss Jordan method 2x_1+x_2+3x_3=1 ; 4x_1+4x_2+7x_3=1 ; 2x_1+5x_2+9x_3=3 Question Question Solve the following system of equations by Gauss Jordan method 2x_1+x_2+3x_3=1 ; 4x_1+4x_2+7x_3=1 ; 2x_1+5x_2+9x_3=3 Topic Gauss elimination method, Gauss Jordan method, Gauss Siedal method Gauss elimination method problems Solve by Gauss elimination method 2x+y+4z=12; 4x+11y-z=33; 8x-3y+2z=20 Solve the following equations by Gauss elimination method x+2y+z=3; 2x+3y+2z=5; 3x-5y+5z=2 Solve the following system of equations by Gauss elimination method x_1+x_2+x_3+x_4=2; 2x_1-x_2+2x_3-x_4=-5; 3x_1+2x_2+3x_3+4x_4=7; x_1-2x_2-3x-3+2x_4=5; Solve…

Solve the following system of equations by Gauss Jordan method. x+y+z=9 ; x-2y+3z=8 ; 2x+y-z=3 Question Question Solve the following system of equations by Gauss Jordan method. x+y+z=9 ; x-2y+3z=8 ; 2x+y-z=3 Topic Gauss elimination method, Gauss Jordan method, Gauss Siedal method Gauss elimination method problems Solve by Gauss elimination method 2x+y+4z=12; 4x+11y-z=33; 8x-3y+2z=20 Solve the following equations by Gauss elimination method x+2y+z=3; 2x+3y+2z=5; 3x-5y+5z=2 Solve the following system of equations by Gauss elimination method x_1+x_2+x_3+x_4=2; 2x_1-x_2+2x_3-x_4=-5; 3x_1+2x_2+3x_3+4x_4=7; x_1-2x_2-3x-3+2x_4=5; Solve…

Solve by Gauss Jordan method the system of linear equation 2x+y+z=10 ; 3x+2y+3z=18 ; x+4y+9z=16 Question Question Solve by Gauss Jordan method the system of linear equation 2x+y+z=10 ; 3x+2y+3z=18 ; x+4y+9z=16 Topic Gauss elimination method, Gauss Jordan method, Gauss Siedal method Gauss elimination method problems Solve by Gauss elimination method 2x+y+4z=12; 4x+11y-z=33; 8x-3y+2z=20 Solve the following equations by Gauss elimination method x+2y+z=3; 2x+3y+2z=5; 3x-5y+5z=2 Solve the following system of equations by Gauss elimination method x_1+x_2+x_3+x_4=2; 2x_1-x_2+2x_3-x_4=-5; 3x_1+2x_2+3x_3+4x_4=7; x_1-2x_2-3x-3+2x_4=5; Solve…