Let a and B be the standard bases for F? and F³ respectively (where F is a field). Let -G:), -() 1 1 (1 2 5 A= 3 4 6 B = 3 4 1 2 Let LA : F3 –→ F² be the linear transformation defined by LẠ(v) = Av....

Let a and B be the standard bases for F? and F³ respectively (where F<br>is a field). Let<br>-G:), -()<br>1 1<br>(1 2 5<br>A=<br>3 4 6<br>B =<br>3 4<br>1 2<br>Let LA : F3 –→ F² be the linear transformation defined by LẠ(v) = Av.<br>Similarly, let LB : F² → F³ be the linear transformation defined by<br>LB(w) = Bw. Verify that<br>(a) [LA]; = A.<br>(b) [LẠLB]a = AB.<br>АВ.<br>

Extracted text: Let a and B be the standard bases for F? and F³ respectively (where F is a field). Let -G:), -() 1 1 (1 2 5 A= 3 4 6 B = 3 4 1 2 Let LA : F3 –→ F² be the linear transformation defined by LẠ(v) = Av. Similarly, let LB : F² → F³ be the linear transformation defined by LB(w) = Bw. Verify that (a) [LA]; = A. (b) [LẠLB]a = AB. АВ.

Jun 04, 2022

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Let a and B be the standard bases for F? and F³ respectively (where F is a field). Let -G:), -() 1 1 (1 2 5 A= 3 4 6 B = 3 4 1 2 Let LA : F3 –→ F² be the linear transformation defined by LẠ(v) = Av....

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