MTH501- Linear Algebra MCQS MIDTERM EXAMINATION ~“LIBRIANSMINE”~ Question No: 1 (Marks: 1) - Please choose one If for a linear transformation the equation T(x) =0 has only the trivial solution then T is One-to-one Onto Question No: 2 (Marks: 1) - Please choose one Which one of the following is an elementary matrix? . A linear transformation (or a linear map) is a function T: R n → R m that satisfies the following properties: T ( x + y) = T ( x) + T ( y) T ( a x) = a T ( x) for any vectors x, y ∈ R n and any scalar a ∈ R. It is simple enough to identify whether or not a given function f ( x) is a linear transformation. Formally, for vector spaces V, W over the same field K, the function Set up two matrices to test the addition property is preserved for S S. And we will learn how to write a least-squares regression equation for the transformed data, as well as how to graph residual plots and determine the coefficient of determination using technology. DefineT: V→Vas T(v) =vf or all v∈V. Or with vector coordinates as input and the corresponding vector coordinates output. has a formula of the form . The translate by − 3 in the x direction is b) y = 3 ( x + 3) − 1. The equation of a circle is given by . Let's take the function f ( x, y) = ( 2 x + y, y, x − 3 y), which is a linear transformation from R 2 to R 3. Students learn that the linear equation y = x, or the diagonal line that passes through the origin, is called the parent graph for the family of linear equations. The graph of this function is shown to the right. Similarly, we say a linear transformation T:

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