# Give the standard matrix of the linear transformation that first sends (x, y, z) to (y, y, z), and rotates this vector 90 degrees counterclockwise about the origin in the x = y plane. Find standard matrix of linear transformation.

Give the standard matrix of the linear transformation that first sends (x, y, z) to (y, y, z), and rotates this vector 90 degrees counterclockwise about the origin in the x = y plane. Find standard matrix of linear transformation.
You can still ask an expert for help

## Want to know more about Matrix transformations?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

niveaus7s
MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document Use a composition: math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> T:${R}^{2}$$\to$${R}^{2}$. $T\left(x,y,z\right)\to \left(y,y,z\right)$. What is the matrix for a rotation of 90 degrees? Not hard to find. Call it $R$:${R}^{2}$$\to$${R}^{2}$ defined by a matrix. (considers sin and cos as a $2×2$ matrix). Using these facts, do you think you could come up with a composition involving the transformations math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> T and math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> R to find the desired linear transformation?