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(4) (a) Fill in the blanks below to give concrete examples of 2 x 2 matrices as asked, no need to explain. • A matrix R such that multiplication by R induces reflection across a line in R². • A matrix S such that S = 27 for all vectors in R². • A matrix T such that multiplication by T sends vectors on the z-axis to 20, but leaves the y-coordinate of all vectors unchanged. Write your answers here: R= ]. s-[ (b) What is the rank of the matrix A= RST? Explain. T-[ ]. ].

(4) (a) Fill in the blanks below to give concrete examples of 2 x 2 matrices as asked, no need to explain. • A matrix R such that multiplication by R induces reflection across a line in R². • A matrix S such that S = 27 for all vectors in R². • A matrix T such that multiplication by T sends vectors on the z-axis to 20, but leaves the y-coordinate of all vectors unchanged. Write your answers here: R= ]. s-[ (b) What is the rank of the matrix A= RST? Explain. T-[ ]. ].

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(4) (a) Fill in the blanks below to give concrete examples of 2 x 2 matrices as asked, no need to explain. A matrix R such that multiplication by R induces reflection across a line in R². . A matrix S such that Sü= 20 for all vectors in R2. A matrix T such that multiplication by T sends vectors on the r-axis to 20, but leaves the y-coordinate of all vectors unchanged. Write your answers here: R= ]. (b) What is the rank of the matrix A= RST? Explain. S= 1₁ T=[ -[ ]
Transcribed Image Text:(4) (a) Fill in the blanks below to give concrete examples of 2 x 2 matrices as asked, no need to explain. A matrix R such that multiplication by R induces reflection across a line in R². . A matrix S such that Sü= 20 for all vectors in R2. A matrix T such that multiplication by T sends vectors on the r-axis to 20, but leaves the y-coordinate of all vectors unchanged. Write your answers here: R= ]. (b) What is the rank of the matrix A= RST? Explain. S= 1₁ T=[ -[ ]
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