Podcast
Questions and Answers
If the matrix $\begin{pmatrix}1 & 2 & \sqrt{6}\0 & 0 & 1\0 & 0 & 0\end{pmatrix} \begin{pmatrix}3 & 0 & 1\6 & -1 & 2\2 & 0 & 1\end{pmatrix}$ is in reduced row echelon form (RREF), then √ is equal to:
If the matrix $\begin{pmatrix}1 & 2 & \sqrt{6}\0 & 0 & 1\0 & 0 & 0\end{pmatrix} \begin{pmatrix}3 & 0 & 1\6 & -1 & 2\2 & 0 & 1\end{pmatrix}$ is in reduced row echelon form (RREF), then √ is equal to:
Consider the linear system: x + y + z = a, 2x + 3y + 3z = 16, 5x + 2y + 3z = 11. If x = -1, y = 2, and z = r is the solution of this system, where a ∈ ℝ and r ∈ ℝ, then a is equal to:
Consider the linear system: x + y + z = a, 2x + 3y + 3z = 16, 5x + 2y + 3z = 11. If x = -1, y = 2, and z = r is the solution of this system, where a ∈ ℝ and r ∈ ℝ, then a is equal to:
The linear system: x + 2y + 5z = 2, 4x + y - 15z = 15, 2x + 3y + 5z = 5 has:
The linear system: x + 2y + 5z = 2, 4x + y - 15z = 15, 2x + 3y + 5z = 5 has:
If z = t, t ∈ ℝ, in the linear system: x + y + 3z = 2, 4x + 5y + 2z = 4, 3x + y + 29z = 14, y is equal to:
If z = t, t ∈ ℝ, in the linear system: x + y + 3z = 2, 4x + 5y + 2z = 4, 3x + y + 29z = 14, y is equal to:
Signup and view all the answers
In the linear system with z = t, t ∈ ℝ as in the previous question, x is equal to:
In the linear system with z = t, t ∈ ℝ as in the previous question, x is equal to:
Signup and view all the answers
In the linear system: x + 2y - z + 3w = -5, 2x + 5y + 2z + 7w = -3, 3x + 8y + 6z + 9w = -2, -2x - 5y + z -12w = -1, the value of w is:
In the linear system: x + 2y - z + 3w = -5, 2x + 5y + 2z + 7w = -3, 3x + 8y + 6z + 9w = -2, -2x - 5y + z -12w = -1, the value of w is:
Signup and view all the answers
The value of z is: _______________
The value of z is: _______________
Signup and view all the answers
Study Notes
Matrix Operations
- A matrix is in reduced row echelon form (RREF) if it meets certain conditions.
- The matrix product [\begin{pmatrix} 1 & 2 & \sqrt{6}\ 0 & 0 & 1\ 0 & 0 & 0 \end{pmatrix} \begin{pmatrix} 3 & 0 & 1\ 6 & -1 & 2\ 2 & 0 & 1 \end{pmatrix}] is in RREF, and √ is equal to 1 + √6.
Linear Systems
- A linear system consists of multiple equations with variables.
- The linear system x + y + z = a, 2x + 3y + 3z = 16, 5x + 2y + 3z = 11 has a solution x = -1, y = 2, and z = r, where a ∈ ℝ and r ∈ ℝ, and a is equal to -5.
- The linear system x + 2y + 5z = 2, 4x + y - 15z = 15, 2x + 3y + 5z = 5 has infinitely many solutions.
- The linear system x + y + 3z = 2, 4x + 5y + 2z = 4, 3x + y + 29z = 14 has a solution z = t, t ∈ ℝ, and y is equal to -4 - 10t, and x is equal to 13 - 6t.
Linear System Applications
- The linear system x + 2y - z + 3w = -5, 2x + 5y + 2z + 7w = -3, 3x + 8y + 6z + 9w = -2, -2x - 5y + z -12w = -1 has a solution with a value of w equal to -1, and a value of z equal to 3.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers concepts of linear algebra, including matrix operations and linear systems. Topics include reduced row echelon form, matrix products, and solving systems of linear equations.
