Math 142–Rodriguez Lehmann–1.2
... b. Find the y-intercept. What does it mean in this situation? c. Find the x-intercept. What does it mean in this situation? ...
... b. Find the y-intercept. What does it mean in this situation? c. Find the x-intercept. What does it mean in this situation? ...
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... Suppose also that W1 ⊆ W2 . Then since v1 ∈ W1 implies that v1 ∈ W2 and W2 is a subspace, then v1 + v2 ∈ W2 and, thus, v1 + v2 ∈ W1 ∪ W2 . A similar result holds for W1 ⊇ W2 (see if you can show this). Finally, it remains to be seen that the zero vector is in W1 ∪ W2 . But this is clear, since the ...
... Suppose also that W1 ⊆ W2 . Then since v1 ∈ W1 implies that v1 ∈ W2 and W2 is a subspace, then v1 + v2 ∈ W2 and, thus, v1 + v2 ∈ W1 ∪ W2 . A similar result holds for W1 ⊇ W2 (see if you can show this). Finally, it remains to be seen that the zero vector is in W1 ∪ W2 . But this is clear, since the ...
Question Sheet 1 1. Let u = (−1,1,2) v = (2,0,3) w = (1,3,12
... (a) Find the area of the parallelogram F formed by u1 , u2 . (b) Convince yourself that the image of F under T , denoted T (F ), is the parallelogram formed by T (u1 ), T (u2 ). Then calculate the area of T (F ). (c) Find det(A). (d) Verify that Area(T (F ))/Area(F )=det(A). This is one conceptual d ...
... (a) Find the area of the parallelogram F formed by u1 , u2 . (b) Convince yourself that the image of F under T , denoted T (F ), is the parallelogram formed by T (u1 ), T (u2 ). Then calculate the area of T (F ). (c) Find det(A). (d) Verify that Area(T (F ))/Area(F )=det(A). This is one conceptual d ...
Sheet 14 - TCD Maths home
... Again, the system can be always solved, hence the vectors span IR 4 . ...
... Again, the system can be always solved, hence the vectors span IR 4 . ...
form Given matrix The determinant is indicated by
... Since Determinants are just numbers, they can be equal to some value, even if there are variables inside. To solve a variable equation, just evaluate the determinant using the processes we have discussed and simplify the algebraic expression. Then, set that expression equal to the value of the deter ...
... Since Determinants are just numbers, they can be equal to some value, even if there are variables inside. To solve a variable equation, just evaluate the determinant using the processes we have discussed and simplify the algebraic expression. Then, set that expression equal to the value of the deter ...
