MATH 290 FINAL Terms & Definitions questions with detailed and verified solutions and with a grade of A+

A ________________ ______________ in the variables a1x1 + ... + anxn = b where each ai and b are real numbers. - ANSlinear equation A linear equation in the variables a1x1 + ... + anxn = b where each ai and b are real numbers. We call the real numbers a1, ..., an the _____________ of the linear equation and the real number b the _____________ _________ of the linear equation. - ANScoefficients; constant term is 5x + 3y = 2 a linear equation? - ANSyes is 2x + 10y + 7z = 7 a linear equation? - ANSyes is sqrt(2)x1 + sin(2/7)x2 + 2020x3 = 0 a linear equation? - ANSyes is 2sqrt(x) + 17y = 11 a linear equation? - ANSno is x + 2y = xy a linear equation? - ANSno is 5x^2 + 3y^2 = 2 a linear equation? - ANSno linear equations (often) have ____________, that is, values of the variables which make the equation true. - ANSsolutions the _______________ __________ to a linear equation a1x1 + ... + anxn = b is the collection of all solutions to the equation. - ANSsolution set we often describe the solution set using ____________ form. - ANSparametric when a variable is assigned a parameter, we call it a ____________ variable. - ANSfree