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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblema 25
Capitolo 7, Problema 25

Let A=[−3−72−950]A = \(\begin{bmatrix}\) -3 & -7 \\ 2 & -9 \\ 5 & 0 \(\end{bmatrix}\) and B=[−5−1003−4]B = \(\begin{bmatrix}\) -5 & -1 \\ 0 & 0 \\ 3 & -4 \(\end{bmatrix}\). Solve each matrix equation for X. 4A + 3B = - 2X

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First, write down the given matrix equation: \(4A + 3B = -2X\).
To solve for \(X\), isolate it by dividing both sides of the equation by \(-2\), which gives: \(X = -\frac{1}{2}(4A + 3B)\).
Next, calculate the matrix \$4A$ by multiplying each element of matrix $A$ by 4.
Then, calculate the matrix \$3B$ by multiplying each element of matrix $B$ by 3.
Add the resulting matrices \$4A$ and \$3B$ element-wise, then multiply the sum by \(-\frac{1}{2}\) to find matrix $X$.

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Matrix Operations

Matrix operations include addition, subtraction, and scalar multiplication, which are essential for manipulating matrices. Understanding how to multiply a matrix by a scalar and add or subtract matrices element-wise is crucial for solving matrix equations like 4A + 3B = -2X.
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Performing Row Operations on Matrices

Solving Matrix Equations

Solving matrix equations involves isolating the unknown matrix by performing inverse operations. For an equation like 4A + 3B = -2X, you must first combine known matrices and then divide or multiply by the inverse scalar to find X.
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Solving Logarithmic Equations

Scalar Multiplication and Division of Matrices

Scalar multiplication involves multiplying every element of a matrix by a constant. To solve for X in -2X = 4A + 3B, you multiply matrices A and B by scalars 4 and 3 respectively, then divide the resulting matrix by -2 to isolate X.
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Introduction to Matrices
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Let A=[−3−72−950]A = \(\begin{bmatrix}\) -3 & -7 \\ 2 & -9 \\ 5 & 0 \(\end{bmatrix}\) and B=[−5−1003−4]B = \(\begin{bmatrix}\) -5 & -1 \\ 0 & 0 \\ 3 & -4 \(\end{bmatrix}\). Solve each matrix equation for X. B - X = 4A

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