Let P be a 6x3 matrix and Q be a 3x6 matrix. Also, let A and B be linear functions A(x)=P(x) and B(y)=Q(y), where x,y are vectors. Fill in the blanks of the question below and explain your answers. 1. A is a function from Rs to Rt, where s=____ and t=____. The matrix of the composition BA equals ____. The null space of P is a subspace of Ra, where a=____. The range of P is a subspace of Rb where b=____.
Let P be a 6x3 matrix and Q be a 3x6 matrix. Also, let A and B be linear functions A(x)=P(x) and B(y)=Q(y), where x,y are vectors. Fill in the blanks of the question below and explain your answers. 1. A is a function from Rs to Rt, where s=____ and t=____. The matrix of the composition BA equals ____. The null space of P is a subspace of Ra, where a=____. The range of P is a subspace of Rb where b=____.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let P be a 6x3 matrix and Q be a 3x6 matrix. Also, let A and B be linear functions A(x)=P(x) and B(y)=Q(y), where x,y are
1. A is a function from Rs to Rt, where s=____ and t=____. The matrix of the composition BA equals ____. The null space of P is a subspace of Ra, where a=____. The range of P is a subspace of Rb where b=____. The largest possible value of the rank(Q) is ____. The smallest possible value of nullity(Q) is ____.
Please indicate any definitions, diagrams or theorems that were used to help solve the problem.
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