How would I do these Matrices?
1.
|1/2 14
10 -8|
2,
Let matrix A = [8 -2
4 7 ]
Let matrix B = 2A, Find b_22
1.
What do you want to do to it? Find the determinant?
If so
(1/2)(-8) - (14)(10)
= -4 -140
= -144
2.
2*7 = 14
Is this right then?
|12 -21
-2 -2/3|
answer-1/50
| 12 -21 |
| -2 -2/3|
12(-2/3) -(-21*-2)
= -8 - 42
= -50
What about this one? Correct?
|1 0
0 1|
The answer would be 1
Yes.
To solve the given matrix problems, we will use basic matrix operations.
For the first problem, we are given a 2x2 matrix:
|1/2 14|
|10 -8|
To perform matrix operations, we can use the following steps for matrix addition, subtraction, and scalar multiplication:
1. Matrix Addition: Add corresponding elements from two matrices.
2. Matrix Subtraction: Subtract corresponding elements from two matrices.
3. Scalar Multiplication: Multiply each element of a matrix by a scalar value.
Now, let's solve the first problem step by step:
1. Matrix Addition:
To add two matrices, say matrix A and matrix B, we need to add their corresponding elements. In this case, we only have one matrix.
The given matrix:
|1/2 14|
|10 -8|
2. Matrix Subtraction:
Similar to matrix addition, we subtract corresponding elements from two matrices. However, we only have one matrix in this case.
The given matrix:
|1/2 14|
|10 -8|
3. Scalar Multiplication:
Scalar multiplication means multiplying each element of a matrix by a scalar. In this case, we do not have to perform scalar multiplication.
The given matrix:
|1/2 14|
|10 -8|
So, here we have performed the basic matrix operations.
Now moving to the second problem:
We are given two matrices, A and B.
Matrix A:
|8 -2|
|4 7|
Matrix B:
B = 2A, which implies that we need to multiply matrix A by 2.
To find the element at the second row and second column in matrix B, i.e., b_22:
1. Multiply each element of matrix A by 2:
2 * |8 -2|
|4 7|
Resulting matrix B:
|16 -4|
|8 14|
The element at the second row and second column in matrix B, b_22, is 14.
So, the answer to the second problem is b_22 = 14.