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DETAILS LARLINALG8 1.R.004. Determine whether the equation is linear in the variables x and y. e-2x...
Determine whether the equation is linear in the variables x and y. у The equation is...
Determine whether the equation is linear in the variables x and y. у The equation is linear in the variables x and y. The equation is not linear in the variables x and y. Need Help? Read it Talk to a Tutor MY NOTES [-/1 Points] LARLINALG8 1.1.007. ASK YOUR TEA DETAILS Find a parametric representation of the solution set of the linear equation. (Enter your answer as a comma-separated list of equations. Use t as your parameter.) 4x -...
DETAILS LARLINALG8 6.R.013. Determine whether the function is a linear transformation. T: R2 – R2, T(x,...
DETAILS LARLINALG8 6.R.013. Determine whether the function is a linear transformation. T: R2 – R2, T(x, y) = (x + h. y + k), h + 0 or k + 0 (translation in R2) linear transformation not a linear transformation If it is, find its standard matrix A. (If an answer does not exist, enter DNE in any cell of the matrix.) 11
DETAILS LARLINALG8 7.R.004. Find the characteristic equation of A, the eigenvalues of A, and a basis...
DETAILS LARLINALG8 7.R.004. Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. --8 1 2 011 005 (a) the characteristic equation of A A= (b) the eigenvalues of A (Enter your answers from smallest to largest.) (2, 22, 2₃) = (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 1 = basis for the eigenspace of 12 basis for the eigenspace of 13...
7. [-12 Points] DETAILS TANFIN11 2.1.009. Determine whether the system of linear equations has one and...
7. [-12 Points] DETAILS TANFIN11 2.1.009. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x - 5y = 31 2x + 3y = -1 O one and only one solution O infinitely many solutions O no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y)...
25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by...
25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by Tv) = Av, where A is as follows. 0 1 -6 1 -1 7 40 0 1 9 1 (a) Find T(0, 3, 2, 1). STEP 1: Use the definition of T to write a matrix equation for TO, 3, 2, 1). T10, 3, 2, 1) = and STEP 2: Use your result from Step 1 to solve for T(0, 3, 2, 1). Ti0,...
DETAILS LARLINALG8 7.1.009. Determine whether x is an eigenvector of A. A= 6 2 2 3...
DETAILS LARLINALG8 7.1.009. Determine whether x is an eigenvector of A. A= 6 2 2 3 (a) x = (1, 0) x is an eigenvector. O x is not an eigenvector. (b) x = (1, 2) x is an eigenvector. x is not an eigenvector. (C) x = (2, 1) x is an eigenvector. x is not an eigenvector. (d) x = (1, -2) x is an eigenvector. x is not an eigenvector.
8. -11 points LARLINALG8 4.5.053. Determine whether is a basis for R S = {0,2,5), (0,...
8. -11 points LARLINALG8 4.5.053. Determine whether is a basis for R S = {0,2,5), (0, 2,5), (0, 0,5) is a basis for S is not a basis for R. 175 is a basis for the write u 19, 2, 15) as a linear combination of the vectors and r e late vector is not an IMPOSSIBLE) Need Help?
DETAILS LARLINALG8 2.R.019. Use an inverse matrix to solve the system of linear equations. 5x1 +...
DETAILS LARLINALG8 2.R.019. Use an inverse matrix to solve the system of linear equations. 5x1 + 4x2 = 6 - x + x2 = -21 (x1, x2) =
DETAILS LARLINALG8 8.4.013. Determine whether S is a basis for c2. S = = {(1, -i),...
DETAILS LARLINALG8 8.4.013. Determine whether S is a basis for c2. S = = {(1, -i), (i, 1)) Sis a basis for c2 S is not a basis for c2
DETAILS LARLINALG8 4.R.023. Determine whether W is a subspace of the vector space V. (Select all...
DETAILS LARLINALG8 4.R.023. Determine whether W is a subspace of the vector space V. (Select all that apply.) W = {f: f(0) = -1}, V = C[-1, 1] W is a subspace of V. W is not a subspace of V because it is not closed under addition. W is not a subspace of V because it is not closed under scalar multiplication.
Determine whether the equation is linear in the variables x and y. у The equation is linear in the variables x and y. The equation is not linear in the variables x and y. Need Help? Read it Talk to a Tutor MY NOTES [-/1 Points] LARLINALG8 1.1.007. ASK YOUR TEA DETAILS Find a parametric representation of the solution set of the linear equation. (Enter your answer as a comma-separated list of equations. Use t as your parameter.) 4x -...
DETAILS LARLINALG8 6.R.013. Determine whether the function is a linear transformation. T: R2 – R2, T(x, y) = (x + h. y + k), h + 0 or k + 0 (translation in R2) linear transformation not a linear transformation If it is, find its standard matrix A. (If an answer does not exist, enter DNE in any cell of the matrix.) 11
DETAILS LARLINALG8 7.R.004. Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. --8 1 2 011 005 (a) the characteristic equation of A A= (b) the eigenvalues of A (Enter your answers from smallest to largest.) (2, 22, 2₃) = (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 1 = basis for the eigenspace of 12 basis for the eigenspace of 13...
7. [-12 Points] DETAILS TANFIN11 2.1.009. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x - 5y = 31 2x + 3y = -1 O one and only one solution O infinitely many solutions O no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y)...
25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by Tv) = Av, where A is as follows. 0 1 -6 1 -1 7 40 0 1 9 1 (a) Find T(0, 3, 2, 1). STEP 1: Use the definition of T to write a matrix equation for TO, 3, 2, 1). T10, 3, 2, 1) = and STEP 2: Use your result from Step 1 to solve for T(0, 3, 2, 1). Ti0,...
DETAILS LARLINALG8 7.1.009. Determine whether x is an eigenvector of A. A= 6 2 2 3 (a) x = (1, 0) x is an eigenvector. O x is not an eigenvector. (b) x = (1, 2) x is an eigenvector. x is not an eigenvector. (C) x = (2, 1) x is an eigenvector. x is not an eigenvector. (d) x = (1, -2) x is an eigenvector. x is not an eigenvector.
8. -11 points LARLINALG8 4.5.053. Determine whether is a basis for R S = {0,2,5), (0, 2,5), (0, 0,5) is a basis for S is not a basis for R. 175 is a basis for the write u 19, 2, 15) as a linear combination of the vectors and r e late vector is not an IMPOSSIBLE) Need Help?
DETAILS LARLINALG8 2.R.019. Use an inverse matrix to solve the system of linear equations. 5x1 + 4x2 = 6 - x + x2 = -21 (x1, x2) =
DETAILS LARLINALG8 8.4.013. Determine whether S is a basis for c2. S = = {(1, -i), (i, 1)) Sis a basis for c2 S is not a basis for c2
DETAILS LARLINALG8 4.R.023. Determine whether W is a subspace of the vector space V. (Select all that apply.) W = {f: f(0) = -1}, V = C[-1, 1] W is a subspace of V. W is not a subspace of V because it is not closed under addition. W is not a subspace of V because it is not closed under scalar multiplication.
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