Question

Consider the matrix A= −2−2 6] [−2−3 5] [3 4−8] [−7−9 18 (all one matrix) (a)...

Consider the matrix A=

−2−2 6]

[−2−3 5]

[3 4−8]

[−7−9 18

(all one matrix)

(a) How many rows ofAcontain a pivot position?

(b) Do the columns ofAspanR4?

(c) Does the equationA ~x=~b have a solution for every~b∈R^4?

(d) Would the equation A~x=~0 have a nontrivial solution?

(e) Are the columns of A linearly independent?

(~x is vector x)

Math   Algebra   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the matrix list x = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. Write...
Consider the matrix list x = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. Write a list comprehension to extract the first column of the matrix [1, 4, 7]. Write another list comprehension to create a vector of twice the square of the middle column.
Answer all of the questions true or false: 1. a) If one row in an echelon...
Answer all of the questions true or false: 1. a) If one row in an echelon form for an augmented matrix is [0 0 5 0 0] b) A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one solution. c) The solution set of b is the set of all vectors of the form u = + p + vh where vh is any solution...
7. Answer the following questions true or false and provide an explanation. • If you think...
7. Answer the following questions true or false and provide an explanation. • If you think the statement is true, refer to a definition or theorem. • If false, give a counter-example to show that the statement is not true for all cases. (a) Let A be a 3 × 4 matrix. If A has a pivot on every row then the equation Ax = b has a unique solution for all b in R^3 . (b) If the augmented...
Let A be a real matrix of 7 × 5 format. Answer the questions following: (1)...
Let A be a real matrix of 7 × 5 format. Answer the questions following: (1) Can the homogeneous system AX = 0 have a non-trivial solution? (2) Can the columns of A form a generating system of R^7? (3) Can the columns of A be linearly independent in R^7? A. Yes, No, No D. No, No, Yes B. Yes, Yes, Yes E. No, No, No C. Yes, No, Yes F. No, Yes, Yes
n x n matrix A, where n >= 3. Select 3 statements from the invertible matrix...
n x n matrix A, where n >= 3. Select 3 statements from the invertible matrix theorem below and show that all 3 statements are true or false. Make sure to clearly explain and justify your work. A= -1 , 7, 9 7 , 7, 10 -3, -6, -4 The equation A has only the trivial solution. 5. The columns of A form a linearly independent set. 6. The linear transformation x → Ax is one-to-one. 7. The equation Ax...
LINEAR ALGEBRA For the matrix B= 1 -4 7 -5 0 1 -4 3 2   ...
LINEAR ALGEBRA For the matrix B= 1 -4 7 -5 0 1 -4 3 2    -6 6    -4 Find all x in R^4 that are mapped into the zero vector by the transformation Bx. Does the vector: 1 0 2 belong to the range of T? If it does, what is the pre-image of this vector?
Refer to the following matrices. A = 1 −8 7 −3 −18 6 5 8 6...
Refer to the following matrices. A = 1 −8 7 −3 −18 6 5 8 6 0 5 8 3 4 8 −2     B = 4 −7 4 0 1 4 9 5 3 −3 0 9 C = 1 0 3 2 8     D = 1 9 −7 0 What is the size of each matrix? A     ____× ____ B     _____× _____ C     ____× ____ D     ____× _____
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and...
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2, 4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p = Tk(R(I(q))) for some k, and find this value of k.
#2. For the matrix A =   1 2 1 2 3 7 4 7...
#2. For the matrix A =   1 2 1 2 3 7 4 7 9   find the following. (a) The null space N (A) and a basis for N (A). (b) The range space R(AT ) and a basis for R(AT ) . #3. Consider the vectors −→x =   k − 6 2k 1   and −→y =   2k 3 4  . Find the number k such that the vectors...
Matrix A= -2 1 0 2 -3 4 5 -6 7 vector u= 1 2 1...
Matrix A= -2 1 0 2 -3 4 5 -6 7 vector u= 1 2 1 a) Is the vector u in Null(A) Explain in detail why b) Is the vectro u in Col( A) Explain in detail why
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT