Exercise M15 Page 354

\[ \begin{vmatrix} 2-x & 1\\ 4 & 2-x \end{vmatrix} = 0 \]

Answer

\[ \begin{align} (2-x)*(2-x)-(4*1) &=0 && \text{(Solve for} x \text{.)}\\ 4-2x-2x+x^2 - 4 &=0 && \text{}\\ x^2 -4x &=0 && \text{(Yielding the solution.)}\\ x(x-4) &=0 && \text{(Subtract x from left sides.)}\\ x=0, x-4 &=0 && \text{(when both conditon = 0)}\\ x=&0 , x=4 \end{align} \]

Let’s Verified

#Let's store information in variable x= 0 so 2-0 = 2
A <- matrix( 
   c(2, 1, 4, 2), # the data elements 
   nrow=2,              # number of rows 
   ncol=2,              # number of columns 
   byrow = TRUE)        # fill matrix by rows 

#Let's store information in variable x= 4 so 2-4 = -2
B <- matrix( 
   c(-2, 1, 4, -2), # the data elements 
   nrow=2,              # number of rows 
   ncol=2,              # number of columns 
   byrow = TRUE)        # fill matrix by rows 
det(A)
## [1] 0
det(B)
## [1] 0

X and Y matrixes are Zero Hence, value of x is 0 and 4