a 1 a a 1 11 (1) Consider the matrix A 1 1 1 (a) Find all values of a such that A is singular (i.e. does not have an inv

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A 1 A A 1 11 1 Consider The Matrix A 1 1 1 A Find All Values Of A Such That A Is Singular I E Does Not Have An Inv 1 (77.64 KiB) Viewed 32 times

a 1 a a 1 11 (1) Consider the matrix A 1 1 1 (a) Find all values of a such that A is singular (i.e. does not have an inverse), by applying row operations to the matrix [ A ]] directly. (b) Consider the linear transformation T:R → R3 defined by T(x) = Ax. Make a sketch of where this transformation sends the unit cube, for a "generic” a. Then, make a sketch of the transformation for each parameter value a found in (a). How does your sketch change for these values? b -1 (c) Consider the matrix B=c b Find all values of the parameters -1 b b, c so that A-1 = B. (2) Let S be a plane in R3 passing through the origin, so that S is a two-dimensional subspace of R3. The reflection across S is the linear transformation T: R3 R3 defined by .TV) = v for any vector v in S, and • T(n) = -ñ whenever ñ is perpendicular to S. Now consider the linear transformation given by T(x) = Ax, where A is the matrix А 1 3 -1 -2 2 -2 2 1 2 1 2 This linear transformation is the reflection across a plane S. Find a basis for S.