Suppose A is a 3 x3 matrix and b is a vector in R3 with the property what Ax- b has a unique solution. Explain why the columns of A must span R3 Choose the correct answer below.
a. The equation has a unique solution so for each pair of vectors x and b there is only one possible matrix A. Therefore the columns of A must span R3
b. The reduced echelon form of A must have a pivot in each row or there would be more than one possible solution for the equation Ax-b. Therefore the columns of A must span R3
c. Matrix A is a square matrix, so when computing Ax, the row-vector rule shows that the columns of A must span IR3
d. When b is written as a linear combination of the columns of A it simplifies to the vector of weights x Therefore the columns of A must span R3

Will give let f(x)=2x and g(x)=[tex]2^{x}[/tex] graph the functions on the same coordinate plane. what are the solutions to the equation f(x)=g(x) ? enter your answers in the boxes x=[? ] or x=[? ]

Students at a high school were asked about their favorite outdoor activity. the results are shown in the two-way frequency table below. fishing camping canoeing skiing total boys 36 44 13 25 118 girls 34 37 22 20 113 total 70 81 35 45 231 select all the statements that are true based on the given table. more girls chose camping as their favorite outdoor activity than boys. more girls chose canoeing as their favorite outdoor activity than those who chose skiing. more boys chose skiing as their favorite outdoor activity than girls. there were more boys surveyed than girls. twice as many students chose canoeing as their favorite outdoor activity than those who chose fishing. more students chose camping as their favorite outdoor activity than the combined number of students who chose canoeing or skiing.

Which number line correctly shows 0.8 + 0.3?