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Linear Algebra

03/25/20

math word problem

The employees from maintenance go for coffee together every day at 9 a.m. On Monday, Hector paid $5.70 for three cartons of milk, three cups of coffee, and seven doughnuts. On Tuesday,... more

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Linear Algebra

03/23/20

Alvin is 11 years younger than Elga. The sum of their ages is 43. What is elgas age?

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Linear Algebra Matrix Determinant

03/22/20

Find the determinants for the matrices:

1. [ 5 4 ] [ 1 6 ] 2. [ 1 5 -3 ] [ -1 -3 3 ] [ 0 4 4 ] 3. 3I (I is a 4x4 matrix) 4. [ -1 -3 0 -3 ] [ 0 0 -1 0 ] [ 1 -1 3 -2 ] [ 3 2 -3 4 ]

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Linear Algebra Matrix Determinant

03/22/20

Compute the determinant of the matrix that's obtained from A by applying the indicated row operation:

Suppose A ∈ M3 is a matrix with det(A) = -2The following row operations:a) R1 - 7R2b) 3R2c) R3 ⇄ R1

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Linear Algebra Matrix True Or False Det

03/22/20

Determine which of the following are true and which are false

There exists a 3 x 3 matrix whose range is the same as its null space. The rank of a matrix is the number of non-zero rows that it has. For all square matrices A, it's true that det(-A) =... more

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Linear Algebra Matrix Null Rank

03/22/20

Compute each of the following quantities

Assume that A and B are 3 x 3 matrices with det(A) = 2 and det(B) = 4 det(AB) det(2A2) det(A-1BT) rank(A) dim(null(B))

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Linear Algebra Matrix Rank

03/22/20

Find a real number x where the matrix has a rank equal to 1.

The matrix is: [ 2 2 0 ] [ 1 1 0 ] [ -1 x 0 ]

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Linear Algebra Matrix Rank Nullity

03/22/20

Compute the rank and nullity of each matrix

1. [ -2 4 ] [ 1 5 ] 2. [ 1 2 -1 ] [ -2 -4 2 ]

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Linear Algebra Math

03/22/20

When asked to find ALL unit vectors perpendicular to the plane of the triangle ABC (R3), how many results should I get?

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Linear Algebra

03/19/20

Find all unit vectors in R^2 which are orthogonal to (−3, 1).

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Linear Algebra

03/19/20

You have 10 people in company X, 10 people in company Y and 10 people in company Z. Next year, you have 7 people in company X, 3 people in company Y and 20 people in company Z.

Knowing that 5 people left Z and 15 people joined Z. How many people left X ? Is it solvable ? If no why ?

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Linear Algebra Math Precalculus Trigonometry

03/16/20

A wheel completes 2.4 revolutions in 3 seconds. What is the angular velocity of the wheel in radians per minute? As simplified fraction.

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Linear Algebra Proofs Vectors

03/12/20

Prove that the set {v + w, v + x, w − x} is always linearly dependent

Let v, w, x ∈ Rn be vectors. Prove that the set {v + w, v + x, w − x} is always linearly dependent (even if {v, w, x} is linearly independent).

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Linear Algebra Proofs Vectors

03/12/20

If the set {v, w, x} is linearly independent, so is {v+w, v+x, w+x}

Let v, w, x ∈ Rn be vectors. Prove that if the set of vectors {v, w, x} is linearly independent, then so is the set {v + w, v + x, w + x}.

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Linear Algebra Vectors Spans

03/12/20

What is the value of t that would result in span((0, 1, −1),(1, 2, 1),(t, −1, 4))

Determine which values of t ∈ R result in span((0, 1, −1),(1, 2, 1),(t, −1, 4)) being(i) a line(ii) a planeor (iii) all of R3

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Linear Algebra Vectors Trueorfalse Spans

03/12/20

Vectors and Span: True or False

(a) The inverse of a rotation matrix [R^θ] is [R^−θ].(b) If the vectors v1, v2, . . ., v3 are such that no two of these vectors are scalar multiples of each other then they must form a linearly... more

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Linear Algebra Vectors Spans

03/12/20

Vector Sets and Span

For each set of vectors, determine whether their span is {0}, a line, a plane, all of R2, or all of R3.A) {(0, 0), (3, 7)}B) {(1, 2),(3, 4)}C) {(0, 1, −2),(2, 1, 0),(1, 1, −1)}

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Linear Algebra Vectors Subspaces

03/12/20

Determine which of the following vector sets are and aren't in subspaces

A) The graph of the function y = 4x - 2 in R2B) The graph of the function y = cos(x) - 1 in R2C) The set of solutions (x, y, z) in the equation 3x - 4y + 2z = 0D) The set {(x, y) ∈ R2 : x ≥ 0 and y... more

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Linear Algebra Matrix Inverse

03/04/20

Inverse Matrix Question

Suppose X and Y are both invertible matrices, and W is a block matrix: W = [ X Z ] [ 0 Y ] Show that W is invertible, and its inverse is:[ X-1 -X-1ZY-1 ] = W-1[ 0 Y -1 ]

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Linear Algebra Matrix Inverse

03/04/20

Finding the Inverse of a Matrix

Suppose x ∈ R.Find the inverse of the following matrix: A = [ 1 1 1 ] [ 0 1 1 ] [ x 0 1 ]

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Linear Algebra Matrix Row Equivalent

03/04/20

Row Equivalent Matrices

Determine whether or not the two matrices are row equivalent: matrix one: [ 1 2 1 ] [ 1 -1 1 ] [ 2 1 2 ] matrix two: [ 0 -2 0 ] [ 1 1 1 ] [ 1 0 1 ]

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Linear Algebra Matrix Inverse Inverse Matrices

03/04/20

Inverse Matrices

Find the inverse of the following matrices if it exists: 1. [ 1 -2 ] [ -3 5 ] 2. [ -2 0 2 ] [ 4 -2 -1 ] [ 0 2 -2 ]

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Linear Algebra Reduced Row Echelon Form

03/04/20

Reduced Row Echelon Form

Compute the reduced row echelon form of each of the follow matrices: (a) [ 2 1 ] [ -3 -2 ] (b) [ 3 -3 -3 ] [ 2 -3 -4 ] (c) [ 2 2 ] [ 3 0 ] [ 1 0 ] (d) [ 1 -2 0 ] [ -2 4 -1 ] [ 2 -4 -1 ]

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Linear Algebra

03/03/20

If u = (1, 4, 2), v = (3, 5, 6) and w = (2, 2, 3) are three vectors in R3, then (u + v) . 5(u - w) is_____

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Linear Algebra

03/03/20

If v= (2, 4, 4) and ‖ k v ‖ = 24, then the value of k is:

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math word problem

Alvin is 11 years younger than Elga. The sum of their ages is 43. What is elgas age?

Find the determinants for the matrices:

Compute the determinant of the matrix that's obtained from A by applying the indicated row operation:

Determine which of the following are true and which are false

Compute each of the following quantities

Find a real number x where the matrix has a rank equal to 1.

Compute the rank and nullity of each matrix

When asked to find ALL unit vectors perpendicular to the plane of the triangle ABC (R3), how many results should I get?

Find all unit vectors in R^2 which are orthogonal to (−3, 1).

You have 10 people in company X, 10 people in company Y and 10 people in company Z. Next year, you have 7 people in company X, 3 people in company Y and 20 people in company Z.

A wheel completes 2.4 revolutions in 3 seconds. What is the angular velocity of the wheel in radians per minute? As simplified fraction.

Prove that the set {v + w, v + x, w − x} is always linearly dependent

If the set {v, w, x} is linearly independent, so is {v+w, v+x, w+x}

What is the value of t that would result in span((0, 1, −1),(1, 2, 1),(t, −1, 4))

Vectors and Span: True or False

Vector Sets and Span

Determine which of the following vector sets are and aren't in subspaces

Inverse Matrix Question

Finding the Inverse of a Matrix

Row Equivalent Matrices

Inverse Matrices

Reduced Row Echelon Form

If u = (1, 4, 2), v = (3, 5, 6) and w = (2, 2, 3) are three vectors in R3, then (u + v) . 5(u - w) is_____

If v= (2, 4, 4) and ‖ k v ‖ = 24, then the value of k is:

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