Slide 1.4
... ROW-VECTOR RULE FOR COMPUTING Ax Likewise, the third entry in Ax can be calculated from the third row of A and the entries in x. If the product Ax is defined, then the ith entry in Ax is the sum of the products of corresponding entries from row i of A and from the vertex x. The matrix with 1s ...
... ROW-VECTOR RULE FOR COMPUTING Ax Likewise, the third entry in Ax can be calculated from the third row of A and the entries in x. If the product Ax is defined, then the ith entry in Ax is the sum of the products of corresponding entries from row i of A and from the vertex x. The matrix with 1s ...
Math 327 Elementary Matrices and Inverse Matrices Definition: An n
... Theorem 2.6: If A and B are m × n matrices, then A is row (column) equivalent to B if and only if there are elementary matrices E1 , e2 , · · · , Ek such that B = Ek Ek−1 · · · E2 E1 A (B = AE1 E2 · · · Ek−1 Ek ) Proof: (row case) If A is row equivalent to B, then B is the result of applying a finit ...
... Theorem 2.6: If A and B are m × n matrices, then A is row (column) equivalent to B if and only if there are elementary matrices E1 , e2 , · · · , Ek such that B = Ek Ek−1 · · · E2 E1 A (B = AE1 E2 · · · Ek−1 Ek ) Proof: (row case) If A is row equivalent to B, then B is the result of applying a finit ...
Lecture notes
... Two vectors will output a scalar, if the first vector is transposed before being multiplied with the second vector (of equal dimension). The row of the first vector is multiplied by the corresponding element of the second vector, and the resulting products are sum up. ...
... Two vectors will output a scalar, if the first vector is transposed before being multiplied with the second vector (of equal dimension). The row of the first vector is multiplied by the corresponding element of the second vector, and the resulting products are sum up. ...
Math 54. Selected Solutions for Week 2 Section 1.4
... Construct a 2 × 2 matrix A such that the solution set of the equation A~x = ~0 is the line in R2 through (4, 1) and the origin. Then, find a vector ~b in R2 such that the solution set of A~x = ~b is not a line in R2 parallel to the solution set of A~x = ~0 . Why does this not contradict Theorem 6? W ...
... Construct a 2 × 2 matrix A such that the solution set of the equation A~x = ~0 is the line in R2 through (4, 1) and the origin. Then, find a vector ~b in R2 such that the solution set of A~x = ~b is not a line in R2 parallel to the solution set of A~x = ~0 . Why does this not contradict Theorem 6? W ...