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Finding a Coordinate Matrix In Exercises
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Elementary Linear Algebra (MindTap Course List)
- Finding a Coordinate Matrix In Exercises 14, find the coordinate matrix x in Rn relative to the standard basis. x=(5,2)arrow_forwardCoordinate Representation in M3,1 In Exercises 4952, find the coordinate matrix of X relative to the standard basis for M3,1. X=[121]arrow_forwardProof 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_forward
- Find 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_forwardFind 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 a Coordinate Matrix In Exercises 510, given the coordinate matrix of x relative to a nonstandard basis B forRn, find the coordinate matrix of xrelative to the standard basis. B={(2,3),(3,2)}[x]B=[14]arrow_forward
- Fill in the blanks. To encode a message, create an invertible matrix A and multiply the row matrices by A (on the right) to obtain the row matrices.arrow_forwardThe Determinant of the Inverse of a Matrix In Exercises 29-32, find |A-1|. Begin by finding A-1, and then evaluate its determinant. Verify your result by finding |A|and then applying the formula from Theorem 3.8, |A-1|=1|A|. A=[112248110]arrow_forwardThe determinant of a matrix product In Exercises 1-6, find (a)|A|,(b)|B|,(c)AB and (d)|AB|.Then verify that |A||B|=|AB|. A=[2142],B=[1101]arrow_forward
- Proof Prove that if matrix A is diagonalizable, then AT is diagonalizable.arrow_forwardThe Determinant of a scalar multiple of a Matrix In Exercises 7-14, use the fact that |cA|=cn|A| to evaluate the determinant of the nn matrix. A=[2464686810]arrow_forwardNonsingular Matrix In Exercises 29 and 30, find x such that the matrix A is Nonsingular. A=[31x1]arrow_forward
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