Recent content by Incognitopad

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    How are the determinants of A and B related? (Do not compute det(A))

    sorry. typo. i meant to write a 4. adding columns/rows into others don't change the determinant, but multiplying a row/column multiplies the determinant by the same factor. 3*4*6 72det(A)=det(B)
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    How are the determinants of A and B related? (Do not compute det(A))

    oh, is it that simple? 3*5*6det(A)=det(B)?
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    How are the determinants of A and B related? (Do not compute det(A))

    Homework Statement Consider the matrices A = a1 a2 a3 b1 b2 b3 c1 c2 c3 and B = 3a1 4a2+5a1 6a3 3b1 4b2+5b1 6b3 3c1 4c2+5c1 6c3 How are the determinants of A and B related? DO NOT COMPUTE det(A)! Homework Equations The Attempt at a...
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    How do i find the missing column of a matrix given the full RREF form?

    bump :(
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    How do i find the missing column of a matrix given the full RREF form?

    Homework Statement I'm given a 4x5 matrix with one missing column. I'm also given the RREF form with no missing columns. Previous parts of the question made me find the row, column, and null basis for the matrix. Now it's asking: d) Find the missing column. (Hint: Are the columns of...
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    Show that BA is an idempotent matrix

    yeah, its just originally without writing it out i assumed (BA)^2 was equal to B^2 * A^2 need to get used to matrix multiplication.
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    Show that BA is an idempotent matrix

    (BA)^2 = (BA)(BA) = BABA once again, WOW that was easy = B(AB)A = B(In)A = B(In*A) = B(A) = BA thanks mark.
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    Show that BA is an idempotent matrix

    Homework Statement A square matrix P is called an idempotent if P^2 = P, Show that if A is n x m and B is m x n, and if AB = In, then BA is an idempotentHomework Equations The Attempt at a Solution I have this one identity I think, but I'm not sure how to use it? If A is m x n, then ImA = A...
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    Show that Q is an idempotent matrix

    Uhhh... ah.. Q^2 = ((I + (I - P) A) P) * ((I + (I - P) A) P) = Ok, I'm just going to leave it expanded. Too complicated this way = (P + AP - PAP)^2 = (PP + PAP - PPAP + APP + APAP - APPAP - PAPP - PAPAP + PAPPAP) = (P + PAP - PAP + AP + APAP - APAP - PAP - PAPAP + PAPAP) = (P + AP - PAP) wow...
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    Show that Q is an idempotent matrix

    Homework Statement A square matrix P is called an idempotent if P^2 = P, Show that if P is an idempotent, so is Q = (P + AP - PAP) for any square matrix A (of the same size as P). Homework Equations The Attempt at a Solution basically I factor, Q = (I + (I - P) A) P then I square it and...
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    What is the Image Height for a Converging Lens and Diverging Lens System?

    Homework Statement A converging lens with a focal length of 30cm and a diverging lens with a focal length of -64cm are 139cm apart. A 4.0cm tall object is 50cm in front of the converging lens. distance between image and diverging lens has been calculated to be -32cm, and it is right...