What is a matrix equation?

Matrix Equations and Data Organization

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•
Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A matrix equation is an equation in which the unknowns are matrices, and it can be expressed in the form [A][X] = [B], where [A] is a coefficient matrix, [X] is the matrix of variables, and [B] is the result matrix.
2.
FLASHCARD QUESTION
Front
What does it mean for a matrix to be invertible?
Back
A matrix is invertible if there exists another matrix such that when multiplied together, they yield the identity matrix. This means the matrix has a non-zero determinant.
3.
FLASHCARD QUESTION
Front
How do you solve a system of linear equations using matrices?
Back
You can solve a system of linear equations by representing it in matrix form [A][X] = [B] and then finding [X] by calculating [X] = [A]⁻¹[B], where [A]⁻¹ is the inverse of matrix [A].
4.
FLASHCARD QUESTION
Front
What is an augmented matrix?
Back
An augmented matrix is a matrix that includes the coefficients of a system of linear equations along with the constants from the equations, typically represented as [A|B].
5.
FLASHCARD QUESTION
Front
What is the determinant of a matrix?
Back
The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties about the matrix, such as whether it is invertible.
6.
FLASHCARD QUESTION
Front
What is the identity matrix?
Back
The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.
7.
FLASHCARD QUESTION
Front
How do you find the value of a variable in a matrix equation?
Back
To find the value of a variable in a matrix equation, isolate the variable by performing matrix operations such as addition, subtraction, multiplication, or finding the inverse.
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