Mathematics, 04.08.2019 19:30 maren17

Which of the following statements are true about scalar multiplication of matrices? you can multiply a matrix of any size by a scalar. for any matrix a, 1 × a = a. for any scalar r, ri = i, where i is the identity matrix. you can scale geometric figures using scalar multiplication. scalar multiplication is a shortcut for repeated addition of the same matrix. scalar multiplication is not possible for matrices that are not square.

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Answer from: ashleypere99

Consider all options:

1. You can multiply a matrix of any size by a scalar. This option is true, because the rule of multiplication matrix by the number k, where k≠0 (according to definition) is

$k\cdot \left(\begin{array}{ccc}a_{11} & \dots & a_{1n}\\& \dots & \\a_{m1} & \dots & a_{mn}\end{array}\right)=\left(\begin{array}{ccc}ka_{11} & \dots & ka_{1n}\\& \dots & \\ka_{m1} & \dots & ka_{mn}\end{array}\right).$

2. For any matrix A, 1 × A = A. This option is true, because according to previous definition

$1\cdot A=1\cdot \left(\begin{array}{ccc}a_{11} & \dots & a_{1n}\\& \dots & \\a_{m1} & \dots & a_{mn}\end{array}\right)=\left(\begin{array}{ccc}1\cdot a_{11} & \dots & 1\cdot a_{1n}\\& \dots & \\1\cdot a_{m1} & \dots & 1\cdot a_{mn}\end{array}\right)=\left(\begin{array}{ccc}a_{11} & \dots & a_{1n}\\& \dots & \\a_{m1} & \dots & a_{mn}\end{array}\right)=A.$

3. For any scalar r, rI = I, where I is the identity matrix. This option is false, for example

$r\cdot \left(\begin{array}{cc}1 &0\\0 & 1\end{array}\right)= \left(\begin{array}{cc}r &0\\0 & r\end{array}\right)\neq \left(\begin{array}{cc}1 &0\\0 & 1\end{array}\right).$

4. You can scale geometric figures using scalar multiplication. Geometric figures consists of points and their coordinates can be considered as matrices. Using scalar multiplication to these matrices you'll get coordinates of image figures.

This option is true.

5. Scalar multiplication is a shortcut for repeated addition of the same matrix. While adding matrices you add the corresponding numbers ( $a_{ij}$ to $a_{ij}$ ), then for each matrix's element you can use multiplication as a shortcut for repeated addition and then get multiplication as a shortcut for repeated addition for whole matrix.

6. Scalar multiplication is not possible for matrices that are not square. This is not true, because the definition says that multiplication matrix by a scalar is possible for all matrices.

correct options are 1, 2, 4 and 5.

Answer from: Quest

part 1 answer = 8

part 2 answer = 72

step-by-step explanation:

part 1 explanation = add all of the numbers, then divide by how many numbers you have. so, 200/25 = 8.

part 2 explanation = not gonna lie, this is hard to explain, so just google how to do it.

Answer from: Quest

the answer for this question is : 360°

step-by-step explanation:

we have been given a triangle we need to tell which one of these is a triangle below to map onto itself.

360° rotation is the complete rotation which eventually leads to the same figure which is given.

the correct will be, that is 360° that will cause the triangle below to map onto itself.

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Which of the following statements are true about scalar multiplication of matrices? you can multipl...