How to extract input from a dynamic matrix in R shiny - html

Question

This is related to an old question about creating a matrix-style input in a shiny app with dynamic dimensions. My goal is to have a matrix of numerical inputs (the dimensions of which are determined by other user inputs), and then pass that matrix to other R commands and print some output from those calculations. I have code that successfully executes everything except that I can only access the user inputs as characters.
Here is an example that sets up the input and just prints a couple cells from the matrix (this works fine, but isn't what I need):
shiny::runApp(list(
ui = pageWithSidebar(
headerPanel("test"),
sidebarPanel(
numericInput(inputId = "nrow",
label = "number of rows",
min = 1,
max = 20,
value = 1),
numericInput(inputId = "ncol",
label = "number of columns",
min = 1,
max = 20,
value = 1)
),
mainPanel(
tableOutput("value"),
uiOutput("textoutput"))
),
server = function(input,output){
isolate({
output$value <-renderTable({
num.inputs.col1 <- paste0("<input id='r", 1:input$nrow, "c", 1, "' class='shiny-bound-input' type='number' value='1'>")
df <- data.frame(num.inputs.col1)
if (input$ncol >= 2){
for (i in 2:input$ncol){
num.inputs.coli <- paste0("<input id='r", 1:input$nrow, "c", i, "' class='shiny-bound-input' type='number' value='1'>")
df <- cbind(df,num.inputs.coli)
}
}
colnames(df) <- paste0("time ",as.numeric(1:input$ncol))
df
}, sanitize.text.function = function(x) x)
})
output$textoutput <- renderUI(paste0("Cells [1,1] and [2,2]: ",input$r1c1,",",input$r2c2))
}
))
However, when I try to do any operation on the inputs in the matrix, such as output$textoutput <- renderUI(as.numeric(paste0(input$r1c1))+as.numeric(paste0(input$r2c2))), I get classic R errors like $ operator is invalid for atomic vectors. I have tried many combinations of 'as.numeric', 'as.character', ect. to try to get it into the correct format. When I check the structure of those input cells, I see that they have an extra 'NULL' attribute that I can't seem to get rid of, but I am unsure if that is the root of the problem.
In short, how do I extract the plain numbers from that matrix? Or is there a better way to do this in shiny? The only other solution I'm aware of is the rhandsontable package, which I would prefer not to use if there is a reasonable alternative.
Any suggestions would be very appreciated. Thank you!
Edit/solution: replacing renderUI and uiOutput with renderPrint and verbatimTextOutput solves the problem. Thank you for the comment, blondeclover!