Suppose a is the matrix for t: r3 → r3 relative to the standard basis. find the diagonal matrix a' for t relative to the basis b'.

Step-by-step explanation:

The first that you must ask is whether or not the matrix is a diagonalizable matrix. If so, you have to find a basis of consisting of eigenvectors of the matrix . To do that first find the eigenvalues of the matrix and the the corresponding eigenspaces to that eigenvalues. This will give you the basis of consisting of eigenvectors of A. Next apply the change of coordinates using the matrix of change of coordinates whose columns are the vectors on the new basis. So we have that

is the matrix of T respect to new basis consisting of eigenvectors of T, and it is a diagonal matrix, and its elements on the diagonal are the eigenvalues.

y=x+2 hope this jdjxhdnzbdjdo

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3