Solve the following matrices (I don't know how to do brackets so I will just use commas to separate the numbers and put them in different lines)
A= 0, -2, 3, 1
-3, 1, 0, 4
0, 5, -2, -1
B= 1, -4
-2, 1
3, 0
C= -1, 0, 2
0, 3, 4
0, 8, -1
E= 1
2
3
4
F= -2, 5
3, 7
0, 9
FIND:
) AE =
b) B+F =
c) BC + F =
d) CB =
e) CC =
AE =
top row 0*1 -2*2+3*3+1*4 = 9
row two -3*1+1*2+0*3+4*4 = 15
row three 0*1+5*2-2*3-1*4 = 0
B+F = S
S11 = 1-2 = -1
S12 = -5+5 = 1
S21 = -2+3 = 1
S22 = 1+7 = 8
S31 = 3+0 = 3
S32 = 0+9 = 9
so Sum is
-1 , 1
1 , 8
3 , 9
First do BC, then add F
B has two columns, C has three rows
so you may not multiply B times C
(C times B would be ok)
ok, now CB = P
P11 = -1*1+0*-2+2*3 = 5
P12 = -1*-4+0*1+2*0 = 4
P21 = 0*1+3*-2+4*3 = 6
P22 = 0*-4+3*1+4*0 = 3
P31 = 0*1+8*-2-1*3 = -19
P33 = 0*-4 +8*1-1*0 = 8
so CB=
5 , 4
6 , 3
-19 , 8
CC
1 , 16 , -4
0 , 41 , 8
0 , 16 , 33
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To solve the given matrix problems, we will use matrix multiplication and addition rules. Let's solve them step by step:
a) To find AE, we need to multiply matrices A and E. Matrix multiplication requires the number of columns in the first matrix to be equal to the number of rows in the second matrix. In this case, both matrices have 4 rows and 1 column, so multiplication is possible.
To multiply a row matrix by a column matrix, we take each element of the row and multiply it with the corresponding element in the column, then add the products.
AE = [0, -2, 3, 1] * [1, 2, 3, 4]
= [0*1 + -2*2 + 3*3 + 1*4]
= [0 + -4 + 9 + 4]
= [9]
So, AE = 9.
b) To find B+F, we need to add matrices B and F. Addition of matrices requires both matrices to have the same dimensions.
B+F = [1, -4] + [-2, 5]
= [1 + -2, -4 + 5]
= [-1, 1]
So, B+F = [-1, 1].
c) To find BC + F, we need to multiply matrix B with matrix C, then add the result to matrix F.
BC = [1, -4] * [ -1, 0, 2
0, 3, 4]
= [(1*-1 + -4*0), (1*0 + -4*3), (1*2 + -4*4)]
= [-1, -12, -14]
BC + F = [-1, -12, -14] + [-2, 5]
= [-1 + -2, -12 + 5, -14]
= [-3, -7, -14]
So, BC + F = [-3, -7, -14].
d) To find CB, we need to multiply matrix C with matrix B.
CB = [ -1, 0, 2] * [1, -4
-2, 1
3, 0]
= [(-1*1 + 0*-2 + 2*3), (-1*-4 + 0*1 + 2*0)]
= [5, 4]
So, CB = [5, 4].
e) To find CC, we need to multiply matrix C with itself.
CC = [ -1, 0, 2] * [ -1, 0, 2
0, 3, 4
0, 8, -1]
= [(-1*-1 + 0*0 + 2*0), (-1*0 + 0*3 + 2*8), (-1*2 + 0*4 + 2*-1)]
= [1, 16, -6]
So, CC = [1, 16, -6].
That's how you solve the given matrices!