Find the rank of the matrix A and the rank of the augmented matrix ( A | B ). A = egin{pmatrix} -2 & -1 & -1 & -2 \ -1 & -1 & -2 & 1 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 end{pmatrix}, B = egin{pmatrix} -1 \ -1 \ 2 \ 0 end{pmatrix} Rank(A) = 2 Rank(A|B) = Classify the system of equations AX = B as consistent or inconsistent. Inconsistent Consistent
Added by Susan A.
Close
Step 1
Matrix \( A \): \[ A = \begin{pmatrix} -2 & -1 & -1 & -2 \\ -1 & -1 & -2 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix} \] Matrix \( B \): \[ B = \begin{pmatrix} -1 \\ -1 \\ 2 \\ 0 \end{pmatrix} \] Augmented matrix \( (A | B) \): \[ (A | B) = Show more…
Show all steps
Your feedback will help us improve your experience
Zhumagali Shomanov and 94 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the rank of the matrix $$\left[\begin{array}{lll} a & b & c \\ 0 & d & e \\ 0 & 0 & f \end{array}\right]$$ where $a, d,$ and $f$ are nonzero, and $b, c,$ and $e$ are arbitrary numbers.
Linear Equations
On the Solutions of Linear Systems; Matrix Algebra
Find the ranks of $A B$ and $A M$ (rank 1 matrix times rank 1 matrix): $$ A=\left[\begin{array}{ll} 1 & 2 \\ 2 & 4 \end{array}\right] \text { and } \quad B=\left[\begin{array}{ccc} 2 & 1 & 4 \\ 3 & 1.5 & 6 \end{array}\right] \text { and } M=\left[\begin{array}{ll} 1 & b \\ c & b c \end{array}\right] $$
Vector Spaces
Solving $A x=0$ and $A x=b$
Construct the corresponding system of linear equations. Use the variables listed above the matrix, in the given order. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution(s). $$\left[\begin{array}{rrrr|r}x & y & z & u & \\1 & 0 & 0 & -4 & -3 \\0 & 1 & 0 & -2 & 1 \\0 & 0 & 1 & 3 & -10\end{array}\right]$$
Systems of Equations and Inequalities
Solving Systems of Equations Using Matrices
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD