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What is the solution to the system of linear equations £1—Xo+ x3 =0, 221 —X2 =2, and —32} +223 =1?
What is the solution to the system of linear equations £1—Xo+ x3 =0, 221 —X2 =2, and —32} +223 =1?
- x1 = -5, x2 = -12, x3 = -7 (correct)
- x1 = -7, x2 = 12, x3 = 7
- x1 = 4, x2 = -12, x3 = -7
- x1 = 20, x2 = -12, x3 = -7
What is the value of h such that the matrix is the augmented matrix of a consistent linear system?
What is the value of h such that the matrix is the augmented matrix of a consistent linear system?
- h = 3/2 (correct)
- h = 38/2
- h = 0
- h can be any real value
What is the condition for the vector b to be in the range of the linear transformation T(x) = Ax?
What is the condition for the vector b to be in the range of the linear transformation T(x) = Ax?
- The vector b is in the null space of A.
- The vector b is a scalar multiple of the vector x.
- The vector b is a linear combination of the columns of A. (correct)
- The vector b is a linear transformation of the vector x.
What is the solution to the vector equation 2x + 2y - 3z = 1, x - 2y + z = -3, and x + y - z = 2?
What is the solution to the vector equation 2x + 2y - 3z = 1, x - 2y + z = -3, and x + y - z = 2?
Suppose T : R² → R³ is a linear transformation. If T(u) = [1, 2, 3] and T(v) = [4, 5, 6], what is T(2u - v)?
Suppose T : R² → R³ is a linear transformation. If T(u) = [1, 2, 3] and T(v) = [4, 5, 6], what is T(2u - v)?
What is the standard matrix of the linear transformation T that maps e₁ to e₁ + e₂ and e₂ to e₂ - 2e₁?
What is the standard matrix of the linear transformation T that maps e₁ to e₁ + e₂ and e₂ to e₂ - 2e₁?
What is the description of the entire solution set to Ax = 0?
What is the description of the entire solution set to Ax = 0?
Is the set of vectors { [|1], [|2], [|3] } linearly independent?
Is the set of vectors { [|1], [|2], [|3] } linearly independent?
Is the linear transformation T(x) = [| -2x₁ + x₂, x₁ + 3x₂ |] one-to-one and/or onto?
Is the linear transformation T(x) = [| -2x₁ + x₂, x₁ + 3x₂ |] one-to-one and/or onto?
Let T : R³ → R² be a linear transformation with standard matrix A. If Ax = b has a solution for every b in R², what can be said about the matrix A?
Let T : R³ → R² be a linear transformation with standard matrix A. If Ax = b has a solution for every b in R², what can be said about the matrix A?
What is the inverse of the matrix A if the solution set to Ax = b is described as x = t[1] + 4s[1] + r[-1]?
What is the inverse of the matrix A if the solution set to Ax = b is described as x = t[1] + 4s[1] + r[-1]?
Let T : R² → R² be a linear transformation with standard matrix A. If T is invertible, what can be said about the matrix A?
Let T : R² → R² be a linear transformation with standard matrix A. If T is invertible, what can be said about the matrix A?
If an m x n matrix has m pivot columns, what can be said about the linear transformation T(x) = Ax?
If an m x n matrix has m pivot columns, what can be said about the linear transformation T(x) = Ax?
If A is an m x n matrix and the equation Ax = b is consistent for some b, what can be concluded about the columns of A?
If A is an m x n matrix and the equation Ax = b is consistent for some b, what can be concluded about the columns of A?
If an n x n matrix has n pivot positions, what can be said about the reduced echelon form of A?
If an n x n matrix has n pivot positions, what can be said about the reduced echelon form of A?
If A and B are m x n matrices, what can be said about the matrices AB^T and A^TB?
If A and B are m x n matrices, what can be said about the matrices AB^T and A^TB?
If A is invertible and r ≠ 0, what can be said about the inverse of (rA)?
If A is invertible and r ≠ 0, what can be said about the inverse of (rA)?
If AB = AC where B and C are n x p matrices, and A is an invertible n x n matrix, what can be concluded about B and C?
If AB = AC where B and C are n x p matrices, and A is an invertible n x n matrix, what can be concluded about B and C?
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