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Practice Questions: Matrices | Mathematics for ACT PDF Download
Q1: Evaluate:
(a)
(b)
(c)
(d)
View AnswerAns: (b)
This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.
Q2: Simplify:
(a)
(b)
(c)
(d)
View AnswerAns: (b)
Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:
The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.
Q3: Simplify the following
(a)
(b)
(c)
(d)
View AnswerAns: (d)
When multplying any matrix by a scalar quantity (3 in our case), we simply multiply each term in the matrix by the scalar.
Therefore, every number simply gets multiplied by 3, giving us our answer.
Q4:
(a)
(b)
(c)
(d)
View AnswerAns: (c)
When multiplying a constant to a matrix, multiply each entry in the matrix by the constant.
Q5: With matrix notation, what does M2x3 x N3x4 equal?
(a) None of the answers are correct
(b) P2x4
(c) P3x4
(d) P3x3
View AnswerAns: (b)
M2x3 x N3x4 = P2x4
In general matrix notation, Mrxc shows that the matrix is named M and r is the number of rows and c is the number of columns. When multiplying two matrices, the number of columns in the first matrix must match the number of rows in the second matrix. In addition, when adding or subtracting matrices, the matrices must be of the same size.
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FAQs on Practice Questions: Matrices - Mathematics for ACT
| 1. What are matrices in mathematics? |  |
Ans. Matrices are rectangular arrays of numbers, symbols, or expressions arranged in rows and columns. They are commonly used to represent and solve systems of linear equations.
| 2. How do you add and subtract matrices? | |
Ans. To add or subtract matrices, you simply add or subtract the corresponding elements in the matrices. The matrices must have the same dimensions for this operation to be valid.
| 3. What is the identity matrix? | |
Ans. The identity matrix is a square matrix where all elements are zero except for the diagonal elements, which are all one. It acts as the equivalent of the number 1 in matrix multiplication.
| 4. Can matrices be multiplied together? | |
Ans. Yes, matrices can be multiplied together, but the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix will have the number of rows of the first matrix and the number of columns of the second matrix.
| 5. How do you find the determinant of a matrix? | |
Ans. The determinant of a matrix is a scalar value that can be calculated using a specific formula based on the elements of the matrix. For a 2x2 matrix, the determinant is calculated by multiplying the top left element by the bottom right element and subtracting the product of the top right and bottom left elements.
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