Solution:
Since the rank of is , the number of unknown
The number of free variables are
Put
has infinitely many solution.
17. Suppose A is the 3x 3 zero matrix (i.e., all the entries are 0). Describe...
Suppose the eigenvalues of a 3x 3 matrix A are λ1-5 λ2-4 andh"4 with corresponding eigenvectors v1 = 0 v' 1 and V' -4 Let Cur Atte x,-1-1 | Find the solution or the equation xk + 1 . AXk for the spected xo, and describe what happens as k→00 Find the solution of the equation xx-1 = A4 choose the correct answer below. @a. ½=(5)kl o lli| | | |+2 This c Suppose the eigenvalues of a 3x 3...
Suppose A is a 3 x 3 matrix that is nilpotent but not zero. So Ak-0 for some k 〉 1 A. Verify that 0 is an eigenvalue of A B. Verify that 0 is the only eigenvalue of A. C. Is it possible that there is an invertible matrix P such that P- AP is diagonal?
Describe the possible echelon forms of the following matrix. A is a 3 x 3 matrix with linearly independent columns. Select all that apply. (Note that leading entries marked with an X may have any nonzero value and starred entries (*) may have any value including zero.) B. A. 0 X * 0 0 X X 0 X C. D. le: X 0 X 0 C X 0 0 0 0 X 0
Solve the equation using the zero-product principle. (x-7)(3x + 1)=0 The solution set is (Use a comma to separate answers as needed.)
By using Matlab, (a) Suppose A is a matrix whose entries are all positive numbers. Write one line that will multiply each column of A by a scalar so that, in the resulting matrix, every column sums to 1. (b) Try this more difficult variation: Suppose that A may have zero entries, and leave a column of A that sums to zero unchanged. please help with this, I tried to use this: A = round(4*rand(4,5)+1) A./sum(A),[size(A,1) 1] but this did...
.3 Suppose the eigenvalues of a 3x3 matrix A are A, 4, , and A 6' %3D with corresponding eigenvectors v,= V2= and v Let -2 -5 6. 11 Find the solution of the equation x Ax, for the specified x, and describe what happens ask-o. 13 Find the solution of the equation X1AX Choose the correct answer below. 4. 1. O A. X=2.(4)* +3. -4 1. 6. -5 -2 -3 O B. X=2.(4)* 0 +3. 1. -5 6. 11...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
12 3-5 2 U 0 0 0 0 3 (2) A matri A is no1 0 (Thi is not the matris A) (2) A matrix A iownuivalent to This is nohe matrix A! 11 pts] Give the rank and nullity of Λ. rank(A)--null(.)-- 4 pts Does Ar have a solution for every rigt-haud-side ector BYes or No Justify your aswer 2 pts Give a gemetric description for the set all veetrswih the property that A has a solution 4 ptsl...
3. Ald 1- Lol 2-6 For giver matrix A, solve the homogeneous equation Ax=0 Write He answer in parametric vector form. Then use the parametric vector form to express the solution as a spanning set. Describe geometrically what he solution Set represents.
4. Suppose the matrix equation Az(t) =#(ty has the property that /2 0 0 D =0 1 0 (0 0 -7, and a change of basis matrix given by T 1 1 P = 1 e 1 Compute the solution f(t), and write down the n-th order differential equation associated to the matrix A 4. Suppose the matrix equation Az(t) =#(ty has the property that /2 0 0 D =0 1 0 (0 0 -7, and a change of basis...