Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary.
-$$\begin{array} { l }
( \log 2 ) x + ( \ln 3 ) y + ( \ln 5 ) z = 4 \
( \ln 3 ) x + ( \log 8 ) y + ( \ln 10 ) z = 11 \
( \log 23 ) x + ( \ln 7 ) y + ( \ln 4 ) z = 15
\end{array}$$
A) $\varnothing$
B) $\{ ( 9.25474,1.35236 , - 0.16880 ) \}$
C) $\{ ( 0.30103,9.0309,1.38629 ) \}$
D) $\{ ( 4.12321,3.91519,1.27440 ) \}$

Question

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary.
-$$\begin{array} { l } 
( \log 2 ) x + ( \ln 3 ) y + ( \ln 5 ) z = 4 \
( \ln 3 ) x + ( \log 8 ) y + ( \ln 10 ) z = 11 \
( \log 23 ) x + ( \ln 7 ) y + ( \ln 4 ) z = 15
\end{array}$$
A) $\varnothing$
B) $\{ ( 9.25474,1.35236 , - 0.16880 ) \}$
C) $\{ ( 0.30103,9.0309,1.38629 ) \}$
D) $\{ ( 4.12321,3.91519,1.27440 ) \}$

Quizplus · Accepted Answer

To solve the system of equations using matrix inverses, we first convert the system into matrix form $AX = B$, where $A$ is the coefficient matrix, $X$ is the column matrix of variables $x, y, z$, and $B$ is the column matrix of constants on the right side of the equations. We then find the inverse of matrix $A$ and multiply it by matrix $B$ to find $X$. Using a graphing calculator to perform these operations with the given logarithmic coefficients results in the solution $x = 9.25474$, $y = 1.35236$, and $z = -0.16880$, which corresponds to choice B.

Use a Graphing Calculator and the Method of Matrix Inverses