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Multiple Choice

What is the definition of a matrix?

• A system of equations

• A collection of numbers arranged in rows and columns

• A type of graph

• A mathematical operation

Multiple Choice

What is the definition of a zero matrix?

• A matrix with all elements equal to one

• A matrix with all elements equal to zero

• A matrix with one element

• A matrix with multiple elements

Multiple Choice

What is the definition of a square matrix?

• A matrix with unequal rows and columns

• A matrix with equal rows and columns

• A matrix with only one row

• A matrix with only one column

Multiple Choice

What is a diagonal matrix?

• A matrix with all elements zero

• A matrix with non-zero elements only on the main diagonal

• A matrix with all elements equal

• A matrix with only one row

Multiple Choice

What is the definition of an upper triangular matrix?

• A matrix with all elements below the main diagonal equal to zero

• A matrix with all elements above the main diagonal equal to zero

• A matrix with all elements on the main diagonal equal to zero

• A matrix with all elements in the first row equal to zero

Multiple Choice

What conditions must be met for matrices A and B to be equal?

• They must have the same dimensions

• They must have the same determinant

• They must have the same eigenvalues

• They must be symmetric

Multiple Choice

What is the result of adding the two matrices A and B shown in the image?

• \(\begin{pmatrix} 1 & 0 & 4 \\ 7 & 0 & -3 \end{pmatrix}\)

• \(\begin{pmatrix} -3 & 0 & 0 \\ -3 & 6 & -5 \end{pmatrix}\)

• \(\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\)

• \(\begin{pmatrix} 2 & 0 & 2 \\ 5 & -3 & 1 \end{pmatrix}\)

Multiple Choice

What is the result of multiplying the matrix A by the scalar -3?

• (3 -3 0; 6 0 12; 1 3 2; -2 0 4)

• (3 3 0; 6 0 12; 1 3 2; -2 0 4)

• (3 -3 0; 6 0 12; 1 3 2; 2 0 4)

• (3 -3 0; 6 0 12; 1 3 2; -2 0 5)

Multiple Choice

What is the result of the matrix multiplication shown in the example?

• -12

• -10

• -15

• -8

Multiple Choice

What is the process to create the first row of the resulting matrix when multiplying two matrices?

• Multiply the first row of matrix A with the first column of matrix B

• Multiply the first row of matrix A with the second column of matrix B

• Multiply the second row of matrix A with the first column of matrix B

• Multiply the first row of matrix A with all columns of matrix B

Multiple Choice

Which number sentence is an example of the associative property?

• 19+8=5x5

• 3x(2x4)=(3x2)x4

• 4x9=9+4

• 6x0=6+0

Multiple Choice

What is the definition of a nilpotent matrix according to the text?

• A matrix that is invertible

• A matrix that becomes zero when raised to a certain power

• A matrix that has a determinant of one

• A matrix that is symmetric

Multiple Choice

What are the properties of matrix multiplication as described in the image?

• Associative property

• Commutative property

• Distributive property

• Identity property

Multiple Choice

What is the first step to input matrix A in the calculator?

• Select mode 6

• Press AC

• Shift 4 Dim

• Enter matrix B

Fill in the Blank

Perform the matrix row operation: $$R_1-2R_3$$

Multiple Choice

What is the result of the operation 3h1 - 2h2?

• 0 -1 -7

• 2 -4 6

• 6 3 -9

• 6 4 -2

Open Ended

Solve the linear systems together by using the values of b for two separate systems, then reducing an appropriate augmented matrix to reduced row echelon form. Write your answer as (x1, x2), (x1, x2) form.