3. Let L: R R' be the linear transformation defined by L(X) = Ax, where A is a 3 x 3 matrix with no zero entries and all of its entries different. (a) Find a matrix A so that 0 is in ker L. (b) Can A be chosen nonsingular? Explain.
3. Let L: R R' be the linear transformation defined by L(X) = Ax, where A is a 3 x 3 matrix with no zero entries and all of its entries different. (a) Find a matrix A so that 0 is in ker L. (b) Can A be chosen nonsingular? Explain.
3. Let L: R R' be the linear transformation defined by L(X) = Ax, where A is a 3 x 3 matrix with no zero entries and all of its entries different. (a) Find a matrix A so that 0 is in ker L. (b) Can A be chosen nonsingular? Explain.
Transcribed Image Text:3. Let L: R R' be the linear transformation defined by
L(X) = Ax, where A is a 3 x 3 matrix with no zero entries
and all of its entries different.
(a) Find a matrix A so that 0
is in ker L.
(b) Can A be chosen nonsingular? Explain.
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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