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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblema 28
Capitolo 7, Problema 28

Solve for X in the matrix equation 3X+A = B where

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1
Rewrite the matrix equation 3X + A = B to isolate 3X. Subtract matrix A from both sides: 3X = B - A.
Understand that matrix subtraction (B - A) involves subtracting corresponding elements of matrices B and A. Ensure that matrices B and A have the same dimensions for this operation to be valid.
Once you have the result of B - A, divide each element of the resulting matrix by 3 to solve for X. This is equivalent to multiplying the matrix by the scalar 1/3.
Verify your solution by substituting X back into the original equation 3X + A = B to ensure both sides are equal.
Remember that matrix operations are only valid if the dimensions of the matrices involved are compatible. Double-check the dimensions of A, B, and X to ensure consistency throughout the process.

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Matrix Operations

Matrix operations, including addition, subtraction, and scalar multiplication, are fundamental in linear algebra. In the context of the equation 3X + A = B, understanding how to manipulate matrices is crucial. For instance, you need to know how to add matrix A to the product of 3 and matrix X to isolate X.
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Performing Row Operations on Matrices

Scalar Multiplication

Scalar multiplication involves multiplying each element of a matrix by a scalar (a single number). In the equation 3X, the scalar 3 multiplies every element of matrix X. This concept is essential for simplifying the equation and solving for X, as it directly affects the values within the matrix.
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Finding Zeros & Their Multiplicity

Isolating Variables

Isolating variables is a key algebraic technique used to solve equations. In the equation 3X + A = B, the goal is to isolate X. This involves rearranging the equation by subtracting matrix A from both sides and then dividing by the scalar 3, which is necessary to find the value of X.
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Equations with Two Variables
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