4. Let $A = \begin{bmatrix} a & 0 & 0 \\ b & -1 & 0 \\ -1 & a & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 2 & 3 \\ 1 & -2 & 1 \\ 1 & -6 & -3 \end{bmatrix}$. Find the values of $a$ and $b$ such that \\ $AB = \begin{bmatrix} 2 & 4 & 6 \\ 0 & 4 & 2 \\ 0 & 0 & 2 \end{bmatrix}$, and hence solve the following system of equations:\\ $x_1 + 2x_2 + 3x_3 = 2$ \\ $x_1 - 2x_2 + x_3 = 8$ \\ $x_1 - 6x_2 - 3x_3 = 12$
Added by Mariano F.
Close
Step 1
$AB = \begin{bmatrix} a & 0 & 0 \\ b & -1 & 0 \\ -1 & a & -1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 1 & -2 & 1 \\ 1 & -6 & -3 \end{bmatrix} = \begin{bmatrix} a & 2a & 3a \\ b-1 & 2b+2 & 3b-1 \\ -2-a & 2a+6 & 3a+4 \end{bmatrix}$ Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 91 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
4. Use Cramer's rule to compute the solutions of the system. a) 5x1 + 7x2 = 3; 2x1 + 4x2 = 1 b) 4x1 + x2 = 6; 3x1 + 2x2 = 7 c) 3x1 - 2x2 = 3; -4x1 + 6x2 = -5
Sri K.
4. a. Write the following augmented matrix in row-echelon form. Make sure that every number in this matrix is an integer. b. Solve the system of equations corresponding to the matrix you derived in part a.
Adi S.
Let $A=\left[\begin{array}{ll}{1} & {2} \\ {5} & {12}\end{array}\right], \mathbf{b}_{1}=\left[\begin{array}{r}{-1} \\ {3}\end{array}\right], \mathbf{b}_{2}=\left[\begin{array}{r}{1} \\ {-5}\end{array}\right], \mathbf{b}_{3}=\left[\begin{array}{l}{2} \\ {6}\end{array}\right]$ and $\mathbf{b}_{4}=\left[\begin{array}{l}{3} \\ {5}\end{array}\right]$ a. Find $A^{-1},$ and use it to solve the four equations $A \mathbf{x}=\mathbf{b}_{1}$ $A \mathbf{x}=\mathbf{b}_{2}, A \mathbf{x}=\mathbf{b}_{3}, A \mathbf{x}=\mathbf{b}_{4}$ b. The four equations in part (a) can be solved by the same set of row operations, since the coefficient matrix is the same in each case. Solve the four equations in part (a) by row reducing the augmented matrix $\left[A \text { b, } \mathbf{b}_{2} \mathbf{b}_{3} \mathbf{b}_{4}\right] .$
Matrix Algebra
The Inverse of a Matrix
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD