5. Give 2 x 2 matrices A so that for any x e R? we have, respectively: a. Ax is the vector whose components are, respectively, the sum and difference of the components of x. *b. Ax is the vector obtained by projecting x onto the line x1 = x2 in R?. c. Axis the vector obtained by first reflecting x across the line x1 = 0 and then reflecting the resulting vector across the line x2 = x1. d. Ax is the vector obtained by projecting x onto the line 2x1 – x2 = 0. *e. Ax is the vector obtained by first projecting x onto the line 2x1 – x2 = 0 and then rotating the resulting vector 7/2 counterclockwise. f. Ax is the vector obtained by first rotating x an angle of 1/2 counterclockwise and then projecting the resulting vector onto the line 2x1 – x2 = 0.
5. Give 2 x 2 matrices A so that for any x e R? we have, respectively: a. Ax is the vector whose components are, respectively, the sum and difference of the components of x. *b. Ax is the vector obtained by projecting x onto the line x1 = x2 in R?. c. Axis the vector obtained by first reflecting x across the line x1 = 0 and then reflecting the resulting vector across the line x2 = x1. d. Ax is the vector obtained by projecting x onto the line 2x1 – x2 = 0. *e. Ax is the vector obtained by first projecting x onto the line 2x1 – x2 = 0 and then rotating the resulting vector 7/2 counterclockwise. f. Ax is the vector obtained by first rotating x an angle of 1/2 counterclockwise and then projecting the resulting vector onto the line 2x1 – x2 = 0.
5. Give 2 x 2 matrices A so that for any x e R? we have, respectively: a. Ax is the vector whose components are, respectively, the sum and difference of the components of x. *b. Ax is the vector obtained by projecting x onto the line x1 = x2 in R?. c. Axis the vector obtained by first reflecting x across the line x1 = 0 and then reflecting the resulting vector across the line x2 = x1. d. Ax is the vector obtained by projecting x onto the line 2x1 – x2 = 0. *e. Ax is the vector obtained by first projecting x onto the line 2x1 – x2 = 0 and then rotating the resulting vector 7/2 counterclockwise. f. Ax is the vector obtained by first rotating x an angle of 1/2 counterclockwise and then projecting the resulting vector onto the line 2x1 – x2 = 0.
Transcribed Image Text:5. Give 2 x 2 matrices A so that for any x e R² we have, respectively:
a. Ax is the vector whose components are, respectively, the sum and difference of the
components of x.
*b. Ax is the vector obtained by projecting x onto the line x1 = x2 in R².
c. Axis the vector obtained by first reflecting x across the line x1 = 0 and then reflecting
the resulting vector across the line x2 = X1.
d. Ax is the vector obtained by projecting x onto the line 2x1 – x2 = 0.
*e. Ax is the vector obtained by first projecting x onto the line 2x1
rotating the resulting vector T /2 counterclockwise.
f. Ax is the vector obtained by first rotating x an angle of n/2 counterclockwise and
then projecting the resulting vector onto the line 2x1 – x2 = 0.
- x2 = 0 and then
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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