MA100 Summer Exam Questions
with Correct Answers 2024 Update
with 100% Guaranteed Pass
What is an orthogonal complement? - Answer-Two vector spaces of Rn are orthogonal
complements if they are orthogonal and their dimensions sum to n
How do you get cartesian descriptions for N(A), CS(A), and RS(A) - Answer-N(A) - let
the rows of a matrix, C, be the columns from a basis of RS(A) and solve Cx=0
RS(A) - let the rows of a matrix, C, be the columns from a basis of N(A) and solve Cx=0
CS(A) - CS(A) = RS(At), so find a basis for N(At) and use the columns as rows for a
matrix, C, then solve Cx=0
How do we know if Ax=b is consistent? - Answer-rho(A)=rho(A|b)
b is contained in CS(A)
How do we know if T: V -> W is a linear transformation? - Answer-If T(a+b) = T(a) +
T(B)
AND
T(αa) = αT(a)
What is the identity transformation of a vector, v? - Answer-When the (A transformation
matrix)=Identity matrix
So T(v) = v
How do you invert a linear transformation? - Answer-T^-1 exists if and only if
A(transformation)^-1 exists
Therefore, A(transformation) must be square and have a non-zero determinant
A(inverse transformation) = A(transformation)^-1
What is the range of T? T: V -> W - Answer-R(T) = {w contained in W | w = T(v) for
some v contained in V}
What is the kernel of T? T: V -> W - Answer-ker(T) = {v contained in V | T(v) = z}
with Correct Answers 2024 Update
with 100% Guaranteed Pass
What is an orthogonal complement? - Answer-Two vector spaces of Rn are orthogonal
complements if they are orthogonal and their dimensions sum to n
How do you get cartesian descriptions for N(A), CS(A), and RS(A) - Answer-N(A) - let
the rows of a matrix, C, be the columns from a basis of RS(A) and solve Cx=0
RS(A) - let the rows of a matrix, C, be the columns from a basis of N(A) and solve Cx=0
CS(A) - CS(A) = RS(At), so find a basis for N(At) and use the columns as rows for a
matrix, C, then solve Cx=0
How do we know if Ax=b is consistent? - Answer-rho(A)=rho(A|b)
b is contained in CS(A)
How do we know if T: V -> W is a linear transformation? - Answer-If T(a+b) = T(a) +
T(B)
AND
T(αa) = αT(a)
What is the identity transformation of a vector, v? - Answer-When the (A transformation
matrix)=Identity matrix
So T(v) = v
How do you invert a linear transformation? - Answer-T^-1 exists if and only if
A(transformation)^-1 exists
Therefore, A(transformation) must be square and have a non-zero determinant
A(inverse transformation) = A(transformation)^-1
What is the range of T? T: V -> W - Answer-R(T) = {w contained in W | w = T(v) for
some v contained in V}
What is the kernel of T? T: V -> W - Answer-ker(T) = {v contained in V | T(v) = z}
