Chapter Nine — Matrix Operations and Calculations
The Humongous Book of Algebra Problems
Double-decker matrices that solve systems
9.38 According to Cramer’s Rule, the solution to a system of two linear equations in
two variables is . Given the system below, identify matrices C,
X, and Y.
Matrix C consists of the system’s coefﬁcients. The x-coefﬁcients comprise the
ﬁrst column of matrix C and the y-coefﬁcients comprise the second.
The remaining matrices, X and Y, are created by replacing individual columns
of C with the column of constants: .
To generate matrix X, replace the ﬁrst column of C with the column of
To generate matrix Y, replace the second column of C with the column of
Note: Problems 9.39–9.41 refer to the system of equations below.
9.39 Use variable elimination to solve the system.
Multiply the ﬁrst equation by 2 and multiply the second equation by –3.
Add the equations of the modiﬁed system and solve for x.
are the numbers
with no variables next
to them—usually found
on the right side of
the equal sign.
the X matrix,
replace the x-
coefcients in C
with the numbers
from across the equal
sign. To get the Y
matrix, replace the
check out Problems