Consider the function, T: P₁ (R) → span (e¹,e²) where T(a + bx) = (a + 2b)e* + (a−b)e²a • Show T is a linear transformation • Find [T] where B Find [TC where R = {1, 2} and C= {e, e²x} (1 + r 1 and C Sox 102x 2x
Consider the function, T: P₁ (R) → span (e¹,e²) where T(a + bx) = (a + 2b)e* + (a−b)e²a • Show T is a linear transformation • Find [T] where B Find [TC where R = {1, 2} and C= {e, e²x} (1 + r 1 and C Sox 102x 2x
Consider the function, T: P₁ (R) → span (e¹,e²) where T(a + bx) = (a + 2b)e* + (a−b)e²a • Show T is a linear transformation • Find [T] where B Find [TC where R = {1, 2} and C= {e, e²x} (1 + r 1 and C Sox 102x 2x
Please give a clear and complete solution. Linear algebra and differential equations
Transcribed Image Text:Consider the function, T: P₁ (R) → spang (e¹,e²)
where T(a + bx) = (a + 2b)e* + (a − b)e²™
• Show T is a linear transformation
• Find [T]
where B
• Find [T]
where B
=
{1, 2} and C = {e, e²}
{1+x,1-x} and C
=
{e* + 4e²*, e²}
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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![Consider the function, T: P₁ (R) → spang (e¹,e²)
where T(a + bx) = (a + 2b)e* + (a − b)e²™
• Show T is a linear transformation
• Find [T]
where B
• Find [T]
where B
=
{1, 2} and C = {e, e²}
{1+x,1-x} and C
=
{e* + 4e²*, e²}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17a3957e-043c-4f8b-aacf-43f0e2cd68af%2F20faaaf1-ace6-4e32-bf83-d791ba640198%2Fe74owc9_processed.png&w=3840&q=75)
