Equality of Matrices Find the values of a and b that make the matrices A and B equal.
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Precalculus: Mathematics for Calculus (Standalone Book)
- Guided Proof Prove that if A is row-equivalent to B, and B is row-equivalent to C, A is row-equivalent to C. Getting Started: to prove that If A is row-equivalent to C, you have to find elementary matrices E1, E2. Ek such that A=EkE2E1C. i Begin by observing that A is row-equivalent to B and B is row-equivalent to C. ii This means that there exist elementary matrices F1F2Fn and G1G2Gm such that A=FnF2F1B and B=GmG2G1C. iii Combine the matrix equations from step ii.arrow_forwardDigital Images A four-level gray scale is shown below. aUse the gray scale to find a 66 matrix that digitally represents the image in the figure. bFind a matrix that represents a darker version of the image in the figure. cThe negative of an image is obtained by reversing light and dark, as in the negative of a photograph. Find the matrix that represents the negative of the image in the figure. How do you change the elements of the matrix to create the negative? dIncrease the contrast of the image by changing each 1 to a 0 and each 2 to a 3 in the matrix you found in part a. Draw the image represented by the resulting matrix. Does this clarify the image? eDraw the image represented by the matrix I. Can you recognize what this is? If you dont, try increasing the contrast. I=[123320030101132300030101133230010101]arrow_forwardVerifying the Inverse of a Matrix Calculate the products AB and BA to verify that B is the inverse of A. A=[131140132]B=[834211101]arrow_forward
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