The following table shows some data from a study on substance use among 10th graders in the United States and Europe.   Smoked Cigarettes Cigarette-Free Totals U.S. x y 12,000 Europe z w 95,000 Total   69,210 107,000 (a) The table leads to a linear system of four equations in four unknowns. What is the system? x  +  y          =  12,000         z  +  w  =  95,000     y      +  w  =  69,210 x  +  y  +  z  +  w  =  107,000   x  +  y          =  12,000         z  +  w  =  95,000     y      +  w  =  69,210 x             +  w  =  107,000   x  +  y          =  12,000     y      +  w  =  95,000         z  +  w  =  69,210 x  +  y  +  z  +  w  =  107,000   x  +  y          =  12,000     y      +  w  =  95,000         z  +  w  =  69,210 x             +  w  =  107,000   Does it have a unique solution? This system has infinitely many solutions.This system has no solution.    This system has a finite number of solutions.This system has one solution. What does this indicate about the missing data? The given data is sufficient to obtain the missing data (x, y, z and w).The given data is insufficient to obtain the missing data (x, y, z and w).     (b) Given that 34,510 more European 10th graders smoked cigarettes than U.S. 10th graders, find the missing data. (x, y, z, w) =

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.