Finding the Image Two Ways In Exercises
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Elementary Linear Algebra (MindTap Course List)
- Proof Let A be an nn square matrix. Prove that the row vectors of A are linearly dependent if and only if the column vectors of A are linearly dependent.arrow_forwardFind the determinant of the matrix in Exercise 16 using the method of expansion by cofactors. Use a the third row and b the first column. 16. [342631478]arrow_forwardFinding the Image Two Ways In Exercises 57 and 58, find T(v)by using a the standard and b the matrix relative to B and B. T:R2R2 T(x,y)=(2y,0),v=(1,3)B={(2,1),(1,0)},B={(1,0),(2,2)}arrow_forward
- Find the determinant of the matrix in Exercise 15 using the method of expansion by cofactors. Use a the second row and b the second column. 15. [321456231]arrow_forwardFinding the Image of a Vector In Exercises 7-10, use the standard matrix for the linear transformation T to find the image of the vector v. T(x,y)=(x+y,xy,2x,2y), v=(3,3)arrow_forwardFinding the Standard Matrix and the Image In Exercises 23-26, a find the standard matrix A for the linear transformation T and b use A to find the image of the vector v. Use a software program or a graphing utility to verify your result. T(x,y,z)=(2x+3yz,3x2z,2xy+z), v=(1,2,1)arrow_forward
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