Find the following matrices: a) A + B. (b) A - B. (c) -4A. A=begin{bmatrix}2 & -10&-2 14 & 12&104&-2&2 end{bmatrix} , B=begin{bmatrix}6 & 10&-2 0 & -12&-4-5&2&-2 end{bmatrix}

Question
Matrices
asked 2021-03-07
Find the following matrices:
a) A + B.
(b) A - B.
(c) -4A.
\(A=\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix} , B=\begin{bmatrix}6 & 10&-2 \\0 & -12&-4\\-5&2&-2 \end{bmatrix}\)

Answers (1)

2021-03-08
Given,
\(A=\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix} , B=\begin{bmatrix}6 & 10&-2 \\0 & -12&-4\\-5&2&-2 \end{bmatrix}\)
a)\(A+B=\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix}+\begin{bmatrix}6 & 10&-2 \\0 & -12&-4\\-5&2&-2 \end{bmatrix}\)
\(=\begin{bmatrix}2+6 & -10+10&-2-2 \\14+0 & 12-12&10-4\\4-5&-2+2&2-2 \end{bmatrix}\)
\(=\begin{bmatrix}8 & 0&-4 \\14 & 0&6\\-1&0&0 \end{bmatrix}\)
Step 2
b)\(A-B=\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix}-\begin{bmatrix}6 & 10&-2 \\0 & -12&-4\\-5&2&-2 \end{bmatrix}\)
\(=\begin{bmatrix}2-6 & -10-10&-2-(-2) \\14-0 & 12-(-12)&10-(-4)\\4-(-5)&-2-2&2-(-2) \end{bmatrix}\)
\(=\begin{bmatrix}-4 & -20&0 \\14 & 24&14\\9&-4&4 \end{bmatrix}\)
c)\(-4A=-4\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix}\)
\(=\begin{bmatrix}-4(2) & -4(-10)&-4(-2) \\-4(14) & -4(12)&-4(10)\\-4(4)&-4(-2)&-4(2) \end{bmatrix}\)
\(=\begin{bmatrix}-8 & 40&8 \\-56 & -48&-40\\-16&8&-8 \end{bmatrix}\)
0

Relevant Questions

asked 2021-02-02
Find the following matrices: a) A + B.
(b) A - B.
(c) -4A.
(d) 3A + 2B.
\(A=\begin{bmatrix}6 & 2 & -3 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 3 \end{bmatrix}\)
asked 2021-01-04
Matrix multiplication is pretty tough- so i will cover that in class. In the meantime , compute the following if
\(A=\begin{bmatrix}2&1&1 \\-1&-1&4 \end{bmatrix} , B=\begin{bmatrix}0 & 2 \\-4 & 1\\2&-3 \end{bmatrix} , C=\begin{bmatrix}6 & -1 \\3 & 0\\-2&5 \end{bmatrix} , D=\begin{bmatrix}2 & -3&4 \\-3& 1&-2 \end{bmatrix}\)
If the operation is not possible , write NOT POSSIBLE and be able to explain why
a)A+B
b)B+C
c)2A
asked 2021-01-31
Find the matrices:
a)A + B
b) A - B
c) -4A
d)3A + 2B
\(A=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix} ,B=\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}\)
asked 2020-12-16
Compute the following
a) \begin{bmatrix}-5 & -4&3&-10&-3&6 \\6&-10&5&9&4&-1 \end{bmatrix}+\begin{bmatrix}-7 & 3&10&0&8&8 \\8&0&4&-3&-8&0 \end{bmatrix}
b) -5\begin{bmatrix}8 & -10&7 \\0 & -9&7\\10&-5&-10\\1&5&-10 \end{bmatrix}
c)\begin{bmatrix}3 & 0&-8 \\6 & -4&-2\\6&0&-8\\-9&-7&-7 \end{bmatrix}^T
asked 2021-01-17
Refer to the following matrices.
\(A=\begin{bmatrix}2 & -3&7&-4 \\-11 & 2&6&7 \\6 & 0&2&7 \\5 & 1&5&-8 \end{bmatrix} B=\begin{bmatrix}3 & -1&2 \\0 & 1&4 \\3 & 2&1 \\-1 & 0&8 \end{bmatrix} , C=\begin{bmatrix}1& 0&3 &4&5 \end{bmatrix} , D =\begin{bmatrix}1\\ 3\\-2 \\0 \end{bmatrix}\)
Identify the row matrix. Matrix C is a row matrix.
asked 2021-02-05
Giventhe following matrices:
\(A=\begin{bmatrix}1 & 2 &9 \\ -1 & 2 &0 \\ 0&0&4 \end{bmatrix} B=\begin{bmatrix}0 & -1 \\ 2 & 6 \end{bmatrix} C=\begin{bmatrix}2 & 1 \\ 0 & 0 \end{bmatrix} D=\begin{bmatrix}1 \\ 2 \\ -4 \end{bmatrix}\)
Identify the following:
a) A-B
b) B+C
c) C-D
d) B-C
asked 2021-01-13
Find A+B
\(A=\begin{bmatrix}7 & -1 \\2 & 9 \\ -7 & -8 \end{bmatrix} ,B=\begin{bmatrix}2 & 5 \\-9 &0 \\ 8 & 6 \end{bmatrix}\)
a) \(\begin{bmatrix}5 & 4 \\11 & 9 \\ -15 & -2 \end{bmatrix}\)
b) \(\begin{bmatrix}5 & -6 \\11 &9 \\ -15 & -14 \end{bmatrix}\)
c) \(\begin{bmatrix}9 & -6 \\-7 & 9 \\ 1 & -14 \end{bmatrix}\)
d) \(\begin{bmatrix}9 & 4 \\-7 &9 \\ 1 & -2 \end{bmatrix}\)
asked 2020-11-08
Classify each of the following matrices according as it is (a) real, (b) symmetric, (c) skew-symmetric, (d) Hermitian, or (e) skew-hermitian, and identify its principal and secondary diagonals.
\(\begin{bmatrix}1 & 0&-i \\ 0 & -2 & 4-i \\ i&4+i&3 \end{bmatrix}\)
\(\begin{bmatrix}7 & 0&4 \\ 0 & -2 & 10 \\ 4&10&5 \end{bmatrix}\)
asked 2021-01-10
If possible , find 2A-4B
\(A=\begin{bmatrix}-3 & 5 & -6 \\ 3 & -5 & -1 \end{bmatrix} , B=\begin{bmatrix}-6 & 8 & -3 \\ 3 & 6 & -2 \end{bmatrix}\)
a. \(\begin{bmatrix}-30 & 42 & -24 \\ 18 & 14 & -10 \end{bmatrix}\)
b. not possible
c. \(\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}\)
d. \(\begin{bmatrix} -9 & 13 & -9 \\ 6 & 1 & -3 \end{bmatrix}\)
c. \(\begin{bmatrix} 18 & -22 & 0 \\ -6 & -34 & 6 \end{bmatrix}\)
asked 2021-02-09
find which of the given matrices are nonsingular.
a) \(\begin{bmatrix}1 & 2 &-3 \\-1 & 2&3 \\ 0 &8&0 \end{bmatrix}\)
b)\(\begin{bmatrix}1 & 2 &-3 \\-1 & 2&3 \\ 0 &1&1 \end{bmatrix}\)
c) \(\begin{bmatrix}1 & 1 &2 \\-1 & 3&4 \\ -5 &7&8 \end{bmatrix}\)
d) \(\begin{bmatrix}1 & 1 &4&-1 \\1 & 2&3&2 \\ -1 &3&2&1\\-2&6&12&-4 \end{bmatrix}\)
...